File:Gzy momenta1.PNG

2018-05-24T16:03:49Z

Zg916:

MRD:zg916

2018-05-24T16:00:07Z

Zg916:

File:Gzy reactive1.PNG

2018-05-24T15:59:48Z

Zg916:

MRD:zg916

2018-05-24T15:59:10Z

MRD:zg916

2018-05-24T15:37:36Z

Zg916: /* Exercise two */

== Exercise one ==

'''Q1''': What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''A''': The gradient of the potential energy surface has two components: the partial derivative with respect to r1 and r2 respectively: Vr1 = <math>{ \partial V(r_1, r_2)\over \partial r_1}</math> and Vr2 = <math>{ \partial V(r_1, r_2)\over \partial r_2}</math>. At minimum, both Vr1 and Vr2 are equal to zero. Transition state is defined as the maximum on the minimum energy path, which means it's a minimum point on potential energy curve. So, both Vr1 and Vr2 are equal to zero as well at a transition structure.

To distinguish between minima and transition structures, curvature should be used. Curvature is the second partial derivative with respect to r1 and r2. For minima and transition structures, Vr1r2 > 0. When Vr1r1•Vr2r2 - V2r1r2 > 0, it's a minimum; when Vr1r1•Vr2r2 - V2r1r2 < 0, it's a saddle point, i.e, a transition structure.

'''Q2''': 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.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy DvsT.PNG|thumb|center|Figure 1. Internuclear Distance vs. Time]] || [[File:Gzy DvsT zoomed.PNG|thumb|center|Figure 2. zoomed in at T.S.]]
|}

•Figure1 and figure1 shows the change in distance between HA, HB and HC. The intercept as shown in figure 2 should indicate the position of transition state. When the initial momenta is set to be and the structure remains on transition state , HA, HB and HC should remain stationary,i.e, the distance should be constant. This means that there should be no vibrations of the distance between HA, HB and HC. By testing different initial distance,the position of transition state can be obtained when there are two straight line as shown in figure 3.

{| class="wikitable" border="1"
| [[File:Gzy 0.90774.PNG|thumb|center|Figure 3. Internuclear Distance vs. Time when the initial distance is 0.90774 Å]]
|}

•Position of transition state : 0.90774 Å

'''Q3''': Comment on how the mep and the trajectory you just calculated differ.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy Dynamic 552.PNG|thumb|center|Figure 4. Dynamic surface plot(552 steps)]] || [[File:Gzy MEP 10000.PNG|thumb|center|Figure 5. MEP surface plot(10000 steps)]]
|}

•As shown in figure 4 and 5, MEP gives a smooth trajectory without observable oscillations because it follows only the lowest energy path, ignoring the oscillations as the momenta is reset to zero for each step. In dynamic method, the trajectory follows the actual reaction pathway, showing the vibrations between atoms. To obtain a full trajectory, MEP needs a lot more steps than Dynamic(10000 vs 552). Because MEP measures the motion in infinitesimal fractions, and the velocity, thus the momentum is set to zero at each fraction.

'''Q3''':Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.

'''A''':
{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! Set!! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| 1 || -1.25 || -2.5 || -99.119 || Reactive || [[File:Gzy set1.PNG|400px|thumb|center|Figure 6. SET 1]] || The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 2 ||-1.5 || -2.0 || -100.456 || Unreactive ||[[File:Gzy set2.PNG|400px|thumb|center|Figure 7. SET 2]] || The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side. This indicates the initial energy is not enough.

|-
| 3 ||-1.5 || -2.5 || -98.956 || Reactive ||[[File:Gzy set3.PNG|400px|thumb|center|Figure 8. SET 3]]
|| The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 4 ||-2.5 || -5.0 || -84.956 || Unreactive || [[File:Gzy set4.PNG|400px|thumb|center|Figure 9. SET 4]]
|| The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side with an oscillating path. This indicates the initial energy is not enough.
|-
| 5 ||-2.5 || -5.2 || -83.416 || Reactive || [[File:Gzy set5.PNG|400px|thumb|center|Figure 10. SET 5]] || The trajectory starts from reactants and reaches the transition state. After falling back towards the reactants side, it recross the energy barrier and reach product with an oscillating path eventually. This shows the initial energy is enough to overcome the energy barrier.
|}

'''Q5''':State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

'''A''':
==== Main Assumptions<ref>Heterogeneous Catalysis, T. Bligaard, J.K. Nørskov, in Chemical Bonding at Surfaces and Interfaces, 2008</ref> ====
•Chemical equilibrium between reactants and activated transition state complex

•Atoms have Boltzmann distributed energy in reactant state

•When applying TST, quantum-tunneling effects are assumed negligible and Born-Oppenheimer approximation is invoked

•Once the system attains the transition state, with a velocity towards the product configuration, it will not reenter the initial state region again

As shown in set4 and set5, it is possible for the system to fall back towards the reactant side and recross the energy barrier. This situation is ignored in TST, which means the predicted rate of reaction using TST should be higher than experiment.
Also, it is possible for quantum tunneling to occur during reaction. Particles that tunnel through the potential barrier should have a lower energy because it undergoes exponential decay inside the barrier. This means that the actual energy may be lower than the predicted one.

== Exercise two ==

'''Q6''': 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?

'''A''':F+H2:

[[File:Gzy F+H2.PNG|500px|thumb|center|Figure 11. PES of F approaching H2]]

This is an exothermic reaction. The energy of reactants is higher than that of products as shown in Fig11.

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-H bond is less that the energy released forming H-F bond.

H+HF:

[[File:Gzy H+HF.PNG|500px|thumb|center|Figure 12. PES of H approaching HF]]

This is an endothermic reaction.The energy of reactants is lower than that of products as shown in Fig12.(this particular graph shows an unreactive scenario due to insufficient initial conditions)

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-F bond is larger that the energy released forming H-H bond.

'''Q7''':Locate the approximate position of the transition state.

'''A''':F+H2:

According to Hammond postulate, the transition state resembles the reactant in an exothermic reaction. This means that in the transition state, H-H should be much smaller than H-F. As shown in Fig11, the transition state should have a H-H bond length around 0.75 Å. By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=0.751 Å, dHF=1.808 Å

H+HF:

According to Hammond postulate, the transition state resembles the product in an endothermic reaction. This means that in the transition state, H-H should be larger than H-F.As shown in Fig12, the transition state should have a H-F bond length around 1.810 Å.By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=0.751 Å, dHF=1.810 Å

'''Q8''': Report the activation energy for both reactions.

'''A''': When the system has 0 initial momenta starts from a structure slightly deviated from the transition state towards the reactants, the system can automatically fall back to reactant side along the potential well.

F+H2:

The initial conditions were set to be dHH=0.761 Å, dHF=1.818 Å with 0 initial momenta. The activation energy can be obtained from the energy vs time graph as shown in fig13.

[[File:Gzy ea1.PNG|500px|thumb|center|Figure 13. Energy vs Time]]

H+HF:

The initial conditions were set to be dHH=0.741 Å, dHF=1.81 Å with 0 initial momenta. The activation energy can be obtained from the energy vs time graph as shown in fig14.

MRD:zg916

2018-05-24T15:36:00Z

Zg916: /* Exercise two */

== Exercise one ==

'''Q1''': What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''A''': The gradient of the potential energy surface has two components: the partial derivative with respect to r1 and r2 respectively: Vr1 = <math>{ \partial V(r_1, r_2)\over \partial r_1}</math> and Vr2 = <math>{ \partial V(r_1, r_2)\over \partial r_2}</math>. At minimum, both Vr1 and Vr2 are equal to zero. Transition state is defined as the maximum on the minimum energy path, which means it's a minimum point on potential energy curve. So, both Vr1 and Vr2 are equal to zero as well at a transition structure.

To distinguish between minima and transition structures, curvature should be used. Curvature is the second partial derivative with respect to r1 and r2. For minima and transition structures, Vr1r2 > 0. When Vr1r1•Vr2r2 - V2r1r2 > 0, it's a minimum; when Vr1r1•Vr2r2 - V2r1r2 < 0, it's a saddle point, i.e, a transition structure.

'''Q2''': 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.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy DvsT.PNG|thumb|center|Figure 1. Internuclear Distance vs. Time]] || [[File:Gzy DvsT zoomed.PNG|thumb|center|Figure 2. zoomed in at T.S.]]
|}

•Figure1 and figure1 shows the change in distance between HA, HB and HC. The intercept as shown in figure 2 should indicate the position of transition state. When the initial momenta is set to be and the structure remains on transition state , HA, HB and HC should remain stationary,i.e, the distance should be constant. This means that there should be no vibrations of the distance between HA, HB and HC. By testing different initial distance,the position of transition state can be obtained when there are two straight line as shown in figure 3.

{| class="wikitable" border="1"
| [[File:Gzy 0.90774.PNG|thumb|center|Figure 3. Internuclear Distance vs. Time when the initial distance is 0.90774 Å]]
|}

•Position of transition state : 0.90774 Å

'''Q3''': Comment on how the mep and the trajectory you just calculated differ.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy Dynamic 552.PNG|thumb|center|Figure 4. Dynamic surface plot(552 steps)]] || [[File:Gzy MEP 10000.PNG|thumb|center|Figure 5. MEP surface plot(10000 steps)]]
|}

•As shown in figure 4 and 5, MEP gives a smooth trajectory without observable oscillations because it follows only the lowest energy path, ignoring the oscillations as the momenta is reset to zero for each step. In dynamic method, the trajectory follows the actual reaction pathway, showing the vibrations between atoms. To obtain a full trajectory, MEP needs a lot more steps than Dynamic(10000 vs 552). Because MEP measures the motion in infinitesimal fractions, and the velocity, thus the momentum is set to zero at each fraction.

'''Q3''':Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.

'''A''':
{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! Set!! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| 1 || -1.25 || -2.5 || -99.119 || Reactive || [[File:Gzy set1.PNG|400px|thumb|center|Figure 6. SET 1]] || The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 2 ||-1.5 || -2.0 || -100.456 || Unreactive ||[[File:Gzy set2.PNG|400px|thumb|center|Figure 7. SET 2]] || The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side. This indicates the initial energy is not enough.

|-
| 3 ||-1.5 || -2.5 || -98.956 || Reactive ||[[File:Gzy set3.PNG|400px|thumb|center|Figure 8. SET 3]]
|| The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 4 ||-2.5 || -5.0 || -84.956 || Unreactive || [[File:Gzy set4.PNG|400px|thumb|center|Figure 9. SET 4]]
|| The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side with an oscillating path. This indicates the initial energy is not enough.
|-
| 5 ||-2.5 || -5.2 || -83.416 || Reactive || [[File:Gzy set5.PNG|400px|thumb|center|Figure 10. SET 5]] || The trajectory starts from reactants and reaches the transition state. After falling back towards the reactants side, it recross the energy barrier and reach product with an oscillating path eventually. This shows the initial energy is enough to overcome the energy barrier.
|}

'''Q5''':State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

'''A''':
==== Main Assumptions<ref>Heterogeneous Catalysis, T. Bligaard, J.K. Nørskov, in Chemical Bonding at Surfaces and Interfaces, 2008</ref> ====
•Chemical equilibrium between reactants and activated transition state complex

•Atoms have Boltzmann distributed energy in reactant state

•When applying TST, quantum-tunneling effects are assumed negligible and Born-Oppenheimer approximation is invoked

•Once the system attains the transition state, with a velocity towards the product configuration, it will not reenter the initial state region again

As shown in set4 and set5, it is possible for the system to fall back towards the reactant side and recross the energy barrier. This situation is ignored in TST, which means the predicted rate of reaction using TST should be higher than experiment.
Also, it is possible for quantum tunneling to occur during reaction. Particles that tunnel through the potential barrier should have a lower energy because it undergoes exponential decay inside the barrier. This means that the actual energy may be lower than the predicted one.

== Exercise two ==

'''Q6''': 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?

'''A''':F+H2:

[[File:Gzy F+H2.PNG|500px|thumb|center|Figure 11. PES of F approaching H2]]

This is an exothermic reaction. The energy of reactants is higher than that of products as shown in Fig11.

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-H bond is less that the energy released forming H-F bond.

H+HF:

[[File:Gzy H+HF.PNG|500px|thumb|center|Figure 12. PES of H approaching HF]]

This is an endothermic reaction.The energy of reactants is lower than that of products as shown in Fig12.(this particular graph shows an unreactive scenario due to insufficient initial conditions)

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-F bond is larger that the energy released forming H-H bond.

'''Q7''':Locate the approximate position of the transition state.

'''A''':F+H2:

According to Hammond postulate, the transition state resembles the reactant in an exothermic reaction. This means that in the transition state, H-H should be much smaller than H-F. As shown in Fig11, the transition state should have a H-H bond length around 0.75 Å. By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=0.751 Å, dHF=1.808 Å

H+HF:

According to Hammond postulate, the transition state resembles the product in an endothermic reaction. This means that in the transition state, H-H should be larger than H-F.As shown in Fig12, the transition state should have a H-F bond length around 0.75 Å.By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=1.808 Å, dHF=0.751 Å

'''Q8''': Report the activation energy for both reactions.

'''A''': When the system has 0 initial momenta starts from a structure slightly deviated from the transition state towards the reactants, the system can automatically fall back to reactant side along the potential well.

F+H2:

The initial conditions were set to be dHH=0.761 Å, dHF=1.818 Å with 0 initial momenta. The activation energy can be obtained from the energy vs time graph as shown in fig13.

[[File:Gzy ea1.PNG|500px|thumb|center|Figure 13. Energy vs Time]]

H+HF:

The initial conditions were set to be dHH=0.741 Å, dHF=1.81 Å with 0 initial momenta. The activation energy can be obtained from the energy vs time graph as shown in fig14.

MRD:zg916

2018-05-24T15:30:00Z

Zg916: /* Exercise two */

== Exercise one ==

'''Q1''': What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''A''': The gradient of the potential energy surface has two components: the partial derivative with respect to r1 and r2 respectively: Vr1 = <math>{ \partial V(r_1, r_2)\over \partial r_1}</math> and Vr2 = <math>{ \partial V(r_1, r_2)\over \partial r_2}</math>. At minimum, both Vr1 and Vr2 are equal to zero. Transition state is defined as the maximum on the minimum energy path, which means it's a minimum point on potential energy curve. So, both Vr1 and Vr2 are equal to zero as well at a transition structure.

To distinguish between minima and transition structures, curvature should be used. Curvature is the second partial derivative with respect to r1 and r2. For minima and transition structures, Vr1r2 > 0. When Vr1r1•Vr2r2 - V2r1r2 > 0, it's a minimum; when Vr1r1•Vr2r2 - V2r1r2 < 0, it's a saddle point, i.e, a transition structure.

'''Q2''': 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.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy DvsT.PNG|thumb|center|Figure 1. Internuclear Distance vs. Time]] || [[File:Gzy DvsT zoomed.PNG|thumb|center|Figure 2. zoomed in at T.S.]]
|}

•Figure1 and figure1 shows the change in distance between HA, HB and HC. The intercept as shown in figure 2 should indicate the position of transition state. When the initial momenta is set to be and the structure remains on transition state , HA, HB and HC should remain stationary,i.e, the distance should be constant. This means that there should be no vibrations of the distance between HA, HB and HC. By testing different initial distance,the position of transition state can be obtained when there are two straight line as shown in figure 3.

{| class="wikitable" border="1"
| [[File:Gzy 0.90774.PNG|thumb|center|Figure 3. Internuclear Distance vs. Time when the initial distance is 0.90774 Å]]
|}

•Position of transition state : 0.90774 Å

'''Q3''': Comment on how the mep and the trajectory you just calculated differ.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy Dynamic 552.PNG|thumb|center|Figure 4. Dynamic surface plot(552 steps)]] || [[File:Gzy MEP 10000.PNG|thumb|center|Figure 5. MEP surface plot(10000 steps)]]
|}

•As shown in figure 4 and 5, MEP gives a smooth trajectory without observable oscillations because it follows only the lowest energy path, ignoring the oscillations as the momenta is reset to zero for each step. In dynamic method, the trajectory follows the actual reaction pathway, showing the vibrations between atoms. To obtain a full trajectory, MEP needs a lot more steps than Dynamic(10000 vs 552). Because MEP measures the motion in infinitesimal fractions, and the velocity, thus the momentum is set to zero at each fraction.

'''Q3''':Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.

'''A''':
{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! Set!! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| 1 || -1.25 || -2.5 || -99.119 || Reactive || [[File:Gzy set1.PNG|400px|thumb|center|Figure 6. SET 1]] || The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 2 ||-1.5 || -2.0 || -100.456 || Unreactive ||[[File:Gzy set2.PNG|400px|thumb|center|Figure 7. SET 2]] || The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side. This indicates the initial energy is not enough.

|-
| 3 ||-1.5 || -2.5 || -98.956 || Reactive ||[[File:Gzy set3.PNG|400px|thumb|center|Figure 8. SET 3]]
|| The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 4 ||-2.5 || -5.0 || -84.956 || Unreactive || [[File:Gzy set4.PNG|400px|thumb|center|Figure 9. SET 4]]
|| The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side with an oscillating path. This indicates the initial energy is not enough.
|-
| 5 ||-2.5 || -5.2 || -83.416 || Reactive || [[File:Gzy set5.PNG|400px|thumb|center|Figure 10. SET 5]] || The trajectory starts from reactants and reaches the transition state. After falling back towards the reactants side, it recross the energy barrier and reach product with an oscillating path eventually. This shows the initial energy is enough to overcome the energy barrier.
|}

'''Q5''':State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

'''A''':
==== Main Assumptions<ref>Heterogeneous Catalysis, T. Bligaard, J.K. Nørskov, in Chemical Bonding at Surfaces and Interfaces, 2008</ref> ====
•Chemical equilibrium between reactants and activated transition state complex

•Atoms have Boltzmann distributed energy in reactant state

•When applying TST, quantum-tunneling effects are assumed negligible and Born-Oppenheimer approximation is invoked

•Once the system attains the transition state, with a velocity towards the product configuration, it will not reenter the initial state region again

As shown in set4 and set5, it is possible for the system to fall back towards the reactant side and recross the energy barrier. This situation is ignored in TST, which means the predicted rate of reaction using TST should be higher than experiment.
Also, it is possible for quantum tunneling to occur during reaction. Particles that tunnel through the potential barrier should have a lower energy because it undergoes exponential decay inside the barrier. This means that the actual energy may be lower than the predicted one.

== Exercise two ==

'''Q6''': 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?

'''A''':F+H2:

[[File:Gzy F+H2.PNG|500px|thumb|center|Figure 11. PES of F approaching H2]]

This is an exothermic reaction. The energy of reactants is higher than that of products as shown in Fig11.

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-H bond is less that the energy released forming H-F bond.

H+HF:

[[File:Gzy H+HF.PNG|500px|thumb|center|Figure 12. PES of H approaching HF]]

This is an endothermic reaction.The energy of reactants is lower than that of products as shown in Fig12.(this particular graph shows an unreactive scenario due to insufficient initial conditions)

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-F bond is larger that the energy released forming H-H bond.

'''Q7''':Locate the approximate position of the transition state.

'''A''':F+H2:

According to Hammond postulate, the transition state resembles the reactant in an exothermic reaction. This means that in the transition state, H-H should be much smaller than H-F. As shown in Fig11, the transition state should have a H-H bond length around 0.75 Å. By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=0.751 Å, dHF=1.808 Å

H+HF:

According to Hammond postulate, the transition state resembles the product in an endothermic reaction. This means that in the transition state, H-H should be larger than H-F.As shown in Fig12, the transition state should have a H-F bond length around 0.75 Å.By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=1.808 Å, dHF=0.751 Å

'''Q8''': Report the activation energy for both reactions.

'''A''': When the system has 0 initial momenta starts from a structure slightly deviated from the transition state towards the reactants, the system can automatically fall back to reactant side along the potential well.

F+H2:

The initial conditions were set to be dHH=0.761 Å, dHF=1.818 Å with 0 initial momenta. The activation energy can be obtained from the energy vs time graph as shown in fig13.

[[File:Gzy ea1.PNG|500px|thumb|center|Figure 13. Energy vs Time]]

File:Gzy ea1.PNG

2018-05-24T15:28:52Z

Zg916:

MRD:zg916

2018-05-24T15:27:46Z

Zg916: /* Exercise two */

== Exercise one ==

'''Q1''': What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''A''': The gradient of the potential energy surface has two components: the partial derivative with respect to r1 and r2 respectively: Vr1 = <math>{ \partial V(r_1, r_2)\over \partial r_1}</math> and Vr2 = <math>{ \partial V(r_1, r_2)\over \partial r_2}</math>. At minimum, both Vr1 and Vr2 are equal to zero. Transition state is defined as the maximum on the minimum energy path, which means it's a minimum point on potential energy curve. So, both Vr1 and Vr2 are equal to zero as well at a transition structure.

To distinguish between minima and transition structures, curvature should be used. Curvature is the second partial derivative with respect to r1 and r2. For minima and transition structures, Vr1r2 > 0. When Vr1r1•Vr2r2 - V2r1r2 > 0, it's a minimum; when Vr1r1•Vr2r2 - V2r1r2 < 0, it's a saddle point, i.e, a transition structure.

'''Q2''': 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.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy DvsT.PNG|thumb|center|Figure 1. Internuclear Distance vs. Time]] || [[File:Gzy DvsT zoomed.PNG|thumb|center|Figure 2. zoomed in at T.S.]]
|}

•Figure1 and figure1 shows the change in distance between HA, HB and HC. The intercept as shown in figure 2 should indicate the position of transition state. When the initial momenta is set to be and the structure remains on transition state , HA, HB and HC should remain stationary,i.e, the distance should be constant. This means that there should be no vibrations of the distance between HA, HB and HC. By testing different initial distance,the position of transition state can be obtained when there are two straight line as shown in figure 3.

{| class="wikitable" border="1"
| [[File:Gzy 0.90774.PNG|thumb|center|Figure 3. Internuclear Distance vs. Time when the initial distance is 0.90774 Å]]
|}

•Position of transition state : 0.90774 Å

'''Q3''': Comment on how the mep and the trajectory you just calculated differ.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy Dynamic 552.PNG|thumb|center|Figure 4. Dynamic surface plot(552 steps)]] || [[File:Gzy MEP 10000.PNG|thumb|center|Figure 5. MEP surface plot(10000 steps)]]
|}

•As shown in figure 4 and 5, MEP gives a smooth trajectory without observable oscillations because it follows only the lowest energy path, ignoring the oscillations as the momenta is reset to zero for each step. In dynamic method, the trajectory follows the actual reaction pathway, showing the vibrations between atoms. To obtain a full trajectory, MEP needs a lot more steps than Dynamic(10000 vs 552). Because MEP measures the motion in infinitesimal fractions, and the velocity, thus the momentum is set to zero at each fraction.

'''Q3''':Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.

'''A''':
{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! Set!! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| 1 || -1.25 || -2.5 || -99.119 || Reactive || [[File:Gzy set1.PNG|400px|thumb|center|Figure 6. SET 1]] || The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 2 ||-1.5 || -2.0 || -100.456 || Unreactive ||[[File:Gzy set2.PNG|400px|thumb|center|Figure 7. SET 2]] || The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side. This indicates the initial energy is not enough.

|-
| 3 ||-1.5 || -2.5 || -98.956 || Reactive ||[[File:Gzy set3.PNG|400px|thumb|center|Figure 8. SET 3]]
|| The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 4 ||-2.5 || -5.0 || -84.956 || Unreactive || [[File:Gzy set4.PNG|400px|thumb|center|Figure 9. SET 4]]
|| The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side with an oscillating path. This indicates the initial energy is not enough.
|-
| 5 ||-2.5 || -5.2 || -83.416 || Reactive || [[File:Gzy set5.PNG|400px|thumb|center|Figure 10. SET 5]] || The trajectory starts from reactants and reaches the transition state. After falling back towards the reactants side, it recross the energy barrier and reach product with an oscillating path eventually. This shows the initial energy is enough to overcome the energy barrier.
|}

'''Q5''':State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

'''A''':
==== Main Assumptions<ref>Heterogeneous Catalysis, T. Bligaard, J.K. Nørskov, in Chemical Bonding at Surfaces and Interfaces, 2008</ref> ====
•Chemical equilibrium between reactants and activated transition state complex

•Atoms have Boltzmann distributed energy in reactant state

•When applying TST, quantum-tunneling effects are assumed negligible and Born-Oppenheimer approximation is invoked

•Once the system attains the transition state, with a velocity towards the product configuration, it will not reenter the initial state region again

As shown in set4 and set5, it is possible for the system to fall back towards the reactant side and recross the energy barrier. This situation is ignored in TST, which means the predicted rate of reaction using TST should be higher than experiment.
Also, it is possible for quantum tunneling to occur during reaction. Particles that tunnel through the potential barrier should have a lower energy because it undergoes exponential decay inside the barrier. This means that the actual energy may be lower than the predicted one.

== Exercise two ==

'''Q6''': 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?

'''A''':F+H2:

[[File:Gzy F+H2.PNG|500px|thumb|center|Figure 11. PES of F approaching H2]]

This is an exothermic reaction. The energy of reactants is higher than that of products as shown in Fig11.

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-H bond is less that the energy released forming H-F bond.

H+HF:

[[File:Gzy H+HF.PNG|500px|thumb|center|Figure 12. PES of H approaching HF]]

This is an endothermic reaction.The energy of reactants is lower than that of products as shown in Fig12.(this particular graph shows an unreactive scenario due to insufficient initial conditions)

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-F bond is larger that the energy released forming H-H bond.

'''Q7''':Locate the approximate position of the transition state.

'''A''':F+H2:

According to Hammond postulate, the transition state resembles the reactant in an exothermic reaction. This means that in the transition state, H-H should be much smaller than H-F. As shown in Fig11, the transition state should have a H-H bond length around 0.75 Å. By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=0.751 Å, dHF=1.808 Å

H+HF:

According to Hammond postulate, the transition state resembles the product in an endothermic reaction. This means that in the transition state, H-H should be larger than H-F.As shown in Fig12, the transition state should have a H-F bond length around 0.75 Å.By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=1.808 Å, dHF=0.751 Å

'''Q8''': Report the activation energy for both reactions.

'''A''': When the system has 0 initial momenta starts from a structure slightly deviated from the transition state towards the reactants, the system can automatically fall back to reactant side along the potential well.

The initial conditions were set to be dHH=0.761 Å, dHF=1.818 Å with 0 initial momenta. The activation energy can be obtained from the energy vs time graph as shown in fig13

MRD:zg916

2018-05-24T15:19:46Z

Zg916: /* Exercise two */

== Exercise one ==

'''Q1''': What value do the different components of the gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''A''': The gradient of the potential energy surface has two components: the partial derivative with respect to r1 and r2 respectively: Vr1 = <math>{ \partial V(r_1, r_2)\over \partial r_1}</math> and Vr2 = <math>{ \partial V(r_1, r_2)\over \partial r_2}</math>. At minimum, both Vr1 and Vr2 are equal to zero. Transition state is defined as the maximum on the minimum energy path, which means it's a minimum point on potential energy curve. So, both Vr1 and Vr2 are equal to zero as well at a transition structure.

To distinguish between minima and transition structures, curvature should be used. Curvature is the second partial derivative with respect to r1 and r2. For minima and transition structures, Vr1r2 > 0. When Vr1r1•Vr2r2 - V2r1r2 > 0, it's a minimum; when Vr1r1•Vr2r2 - V2r1r2 < 0, it's a saddle point, i.e, a transition structure.

'''Q2''': 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.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy DvsT.PNG|thumb|center|Figure 1. Internuclear Distance vs. Time]] || [[File:Gzy DvsT zoomed.PNG|thumb|center|Figure 2. zoomed in at T.S.]]
|}

•Figure1 and figure1 shows the change in distance between HA, HB and HC. The intercept as shown in figure 2 should indicate the position of transition state. When the initial momenta is set to be and the structure remains on transition state , HA, HB and HC should remain stationary,i.e, the distance should be constant. This means that there should be no vibrations of the distance between HA, HB and HC. By testing different initial distance,the position of transition state can be obtained when there are two straight line as shown in figure 3.

{| class="wikitable" border="1"
| [[File:Gzy 0.90774.PNG|thumb|center|Figure 3. Internuclear Distance vs. Time when the initial distance is 0.90774 Å]]
|}

•Position of transition state : 0.90774 Å

'''Q3''': Comment on how the mep and the trajectory you just calculated differ.

'''A''':
{| class="wikitable" border="1"
| [[File:Gzy Dynamic 552.PNG|thumb|center|Figure 4. Dynamic surface plot(552 steps)]] || [[File:Gzy MEP 10000.PNG|thumb|center|Figure 5. MEP surface plot(10000 steps)]]
|}

•As shown in figure 4 and 5, MEP gives a smooth trajectory without observable oscillations because it follows only the lowest energy path, ignoring the oscillations as the momenta is reset to zero for each step. In dynamic method, the trajectory follows the actual reaction pathway, showing the vibrations between atoms. To obtain a full trajectory, MEP needs a lot more steps than Dynamic(10000 vs 552). Because MEP measures the motion in infinitesimal fractions, and the velocity, thus the momentum is set to zero at each fraction.

'''Q3''':Complete the table by adding a column with the total energy, and another column reporting if the trajectory is reactive or unreactive. For each set of initial conditions, provide a plot of the trajectory and a small description for what happens along the trajectory.

'''A''':
{| class="wikitable" border="1"
|+ Effect of momenta on reactivity
! Set!! p1 !! p2 !! Total energy !! Type of trajectory !! contour plot !! Description
|-
| 1 || -1.25 || -2.5 || -99.119 || Reactive || [[File:Gzy set1.PNG|400px|thumb|center|Figure 6. SET 1]] || The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 2 ||-1.5 || -2.0 || -100.456 || Unreactive ||[[File:Gzy set2.PNG|400px|thumb|center|Figure 7. SET 2]] || The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side. This indicates the initial energy is not enough.

|-
| 3 ||-1.5 || -2.5 || -98.956 || Reactive ||[[File:Gzy set3.PNG|400px|thumb|center|Figure 8. SET 3]]
|| The trajectory starts from reactants, passing through the transition state and reach product. This shows the initial energy is enough to overcome the energy barrier.
|-
| 4 ||-2.5 || -5.0 || -84.956 || Unreactive || [[File:Gzy set4.PNG|400px|thumb|center|Figure 9. SET 4]]
|| The trajectory starts from reactants, after reaching the transition state, it falls back to the reactants side with an oscillating path. This indicates the initial energy is not enough.
|-
| 5 ||-2.5 || -5.2 || -83.416 || Reactive || [[File:Gzy set5.PNG|400px|thumb|center|Figure 10. SET 5]] || The trajectory starts from reactants and reaches the transition state. After falling back towards the reactants side, it recross the energy barrier and reach product with an oscillating path eventually. This shows the initial energy is enough to overcome the energy barrier.
|}

'''Q5''':State what are the main assumptions of Transition State Theory. Given the results you have obtained, how will Transition State Theory predictions for reaction rate values compare with experimental values?

'''A''':
==== Main Assumptions<ref>Heterogeneous Catalysis, T. Bligaard, J.K. Nørskov, in Chemical Bonding at Surfaces and Interfaces, 2008</ref> ====
•Chemical equilibrium between reactants and activated transition state complex

•Atoms have Boltzmann distributed energy in reactant state

•When applying TST, quantum-tunneling effects are assumed negligible and Born-Oppenheimer approximation is invoked

•Once the system attains the transition state, with a velocity towards the product configuration, it will not reenter the initial state region again

As shown in set4 and set5, it is possible for the system to fall back towards the reactant side and recross the energy barrier. This situation is ignored in TST, which means the predicted rate of reaction using TST should be higher than experiment.
Also, it is possible for quantum tunneling to occur during reaction. Particles that tunnel through the potential barrier should have a lower energy because it undergoes exponential decay inside the barrier. This means that the actual energy may be lower than the predicted one.

== Exercise two ==

'''Q6''': 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?

'''A''':F+H2:

[[File:Gzy F+H2.PNG|500px|thumb|center|Figure 11. PES of F approaching H2]]

This is an exothermic reaction. The energy of reactants is higher than that of products as shown in Fig11.

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-H bond is less that the energy released forming H-F bond.

H+HF:

[[File:Gzy H+HF.PNG|500px|thumb|center|Figure 12. PES of H approaching HF]]

This is an endothermic reaction.The energy of reactants is lower than that of products as shown in Fig12.(this particular graph shows an unreactive scenario due to insufficient initial conditions)

The bond strength of H-F is higher than H-H. This is in consistent with the experiment results, because the energy need to break the H-F bond is larger that the energy released forming H-H bond.

'''Q7''':Locate the approximate position of the transition state.

'''A''':F+H2:

According to Hammond postulate, the transition state resembles the reactant in an exothermic reaction. This means that in the transition state, H-H should be much smaller than H-F. As shown in Fig11, the transition state should have a H-H bond length around 0.75 Å. By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=0.751 Å, dHF=1.808 Å

H+HF:

According to Hammond postulate, the transition state resembles the product in an endothermic reaction. This means that in the transition state, H-H should be larger than H-F.As shown in Fig12, the transition state should have a H-F bond length around 0.75 Å.By testing different value of H-H and H-F, the approximate position of the transition state can be obtained when the intermolecular distance is closest to constant given 0 initial momenta.

The approximate position should be dHH=1.808 Å, dHF=0.751 Å

'''Q8''': Report the activation energy for both reactions.

'''A''': When the system starts from a structure slightly

MRD:zg916