MRD:saramalek

2018-05-18T14:17:24Z

Smn216: /* H + HF */

== H + H2 system ==

=== Gradient of the potential energy surface ===

dV/dr = 0 (where r= r1 and r2 i.e. both partial derivatives = 0) at minimum points and transition structures (saddle points), as a zero gradient represents turning points. A minimum point and saddle point can be distinguished by taking the second partial derivative test; the Hessian determinant ,D, is calculated. If:
*D<0 : Saddle point.
*D>0 AND the second partial derivative is >0.

=== Locating the transition state ===

rts=r1 = r2 = 0.908 Å 

{| class="wikitable" border="1"
! Internuclear Distance VS Time Graph !! Analysis
|-
| [[File:TS_H2_distances.jpeg|thumb|center]] || The graph shows two approximately linear lines i.e. there is no/very little oscillation in energy (symmetric vibration of AB and AC)

|}

=== Reaction path ===

{| class="wikitable" border="1"
! MEP !! Dynamic !! Comparison
|-
| [[File:Rxn_path_MEP.jpeg|thumb|center]] || [[File:Reaction_path_dynamic.jpeg|thumb|center]] || The dynamic contour plot shows an oscillating trajectory as opposed to the straight trajectory in the MEP contour plot - this oscillations are due to vibrations of the molecule and there are none present in the MEP plot because it is the lowest energy path and thus oscillations are ignored.

|}

=== Reactive and unreactive trajectories ===

{| class="wikitable" border="1"
! p1 !! p2 !! Total Energy !! Plot of Trajectory !! Unreactive or Reactive
|-
| -1.25 || -2.5 ||-99.018 ||[[File:Smn_H2_trajectories1.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight.
|-
| -1.5 || -2.0 || -100.456 ||[[File:Smn_H2_trajectories2.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is oscillating before and after the TS.
|-
| -1.5 || -2.5 || -98.956||[[File:Smn_H2_trajectories3.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory is oscillating from the start, i.e. from the reactants.
|-
| -2.5 || -5.0 || -84.956||[[File:Smn_H2_trajectories4.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is straight before the TS but when it returns to the reactants, the molecule is vibrating - the oscillations are of high amplitude.
|-
| -2.5 || -5.2 || -83.416||[[File:Smn_H2_trajectories5.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight - the oscillations are of high amplitude.

|}

=== Transition State Theory ===

*Assumptions:
#The reactants will go through a saddle point in the potential energy surface (transition state) and proceed to the products
#The transition state will be in (quasi) equilibrium with the reactants
#

== F-H-H System ==

=== PES Inspection ===

*The H-F bond is stronger than the H2 bond due to the large electronegativity difference between H and F, which polarises the bond introducing strong ionic character.
*Therefore, the 'F + H2' reaction will be exothermic (as it includes making a strong bond and breaking a relatively weak one) and the 'H + HF' system will be endothermic (as the strong H-F bond needs to be broken).
*As 'F + H2' is higher in energy, it is closer in energy to the transition state, according to Hammond's postulate - i.e. in an exothermic reaction the transition state will resemble the reactants (energetically and structurally).
*The surface plot shows the position of the transition state (black dot) - the energy of the transition state is -103.752.

[[File:Smn_fhh_Surface_Plot_transitionstate.jpeg|thumb|center]]
*The Internuclear distance Vs time graph below shows the F-H and H-H bond lengths at the transition state; F-H=A-B= 1.810 and H-H=BC=0.745. The plot shows the transition state because they do not oscillate with time.
[[File:smn_FHH_dvt_TS.jpeg|thumb|center]]

*EA= E(TS) - E(Reactants)
**Performed an MEP with 500000 steps, with the F-H = 1.9 Å (slightly distorted from TS) and H-H= 0.74 Å. When the reactants are F and H2:
***EA = -103.752 - - 104.008 = +0.256 kcalmol-1EXO
**Performed an MEP with 500000 steps, with the F-H = 1.8 Å and H-H= 0.8 Å (slightly distorted from TS). When the reactants are H and H-F:
***EA = -103.752 - - 103.877 = -0.125 kcalmol-1 ENDO

== Reaction dynamics ==

=== Reactive trajectory of F and H-H ===
*exothermic reaction
*to conserve E, the E released is used to vibrate the F-H molecule
*check the IR frequencies of F-H and H-H ~ intensities

[[File:Smn_momentum_FHH.jpeg|thumb|center]]

*momentum vs time plot shows that H-H is constant whereas F-H has an oscillating momentum.

[[File:Smn_energy_fhh_rxndynamics.jpeg]]

=== Polanyis Rules ===
Polanyi's rules state that vibrational energy activates a late transition state more efficiently than translational energy, and the opposite is true for an early transition states.

===F + H2===
*An exothermic reaction with an early transition state. - polanyis predicts that translational is more efficient in crossing barrier.
**F-H momentum = translational (fixed at -0.5)
**H-H momentum = vibrational
*When momentum = 0.3, i.e. less than translational, the trajectory is reactive.
[[File:Smn_momentum_HH_0.3.jpeg|thumb|center|p(H-H) = 0.3]]

*When momentum = 3, i.e. more than translational, the trajectory is unreactive.
[[File:Smn_momentum_HH_3.jpeg|thumb|center|p(H-H) = 3]]

===H + HF===
*An endothermic reaction with a late transition state. - polanyis predicts that vibrational is more efficient in crossing barrier.
**F-H momentum = vibrational energy
**H-H momentum = translational energy
**low H-F momentum (vibrational) - 0.1 and high H-H momentum (translational):
[[File:Smn_HFH_contour_plot.jpeg|thumb|center|p(HF)=0.1 p(HH)=-5]]
**No matter how much the H-H momentum is increased, i.e. the translational energy, the trajectory will recross the barrier and return to reactants. This is because the vibrational energy, F-H momentum, is insufficient for the reaction therefore it follows Polanyis rules because it agrees that vibrational energy is more efficient for crossing late transition states.

2018-05-18T12:58:50Z

Smn216: /* Polanyis Rules */

== H + H2 system ==

=== Gradient of the potential energy surface ===

dV/dr = 0 (where r= r1 and r2 i.e. both partial derivatives = 0) at minimum points and transition structures (saddle points), as a zero gradient represents turning points. A minimum point and saddle point can be distinguished by taking the second partial derivative test; the Hessian determinant ,D, is calculated. If:
*D<0 : Saddle point.
*D>0 AND the second partial derivative is >0.

=== Locating the transition state ===

rts=r1 = r2 = 0.908 Å 

{| class="wikitable" border="1"
! Internuclear Distance VS Time Graph !! Analysis
|-
| [[File:TS_H2_distances.jpeg|thumb|center]] || The graph shows two approximately linear lines i.e. there is no/very little oscillation in energy (symmetric vibration of AB and AC)

|}

=== Reaction path ===

{| class="wikitable" border="1"
! MEP !! Dynamic !! Comparison
|-
| [[File:Rxn_path_MEP.jpeg|thumb|center]] || [[File:Reaction_path_dynamic.jpeg|thumb|center]] || The dynamic contour plot shows an oscillating trajectory as opposed to the straight trajectory in the MEP contour plot - this oscillations are due to vibrations of the molecule and there are none present in the MEP plot because it is the lowest energy path and thus oscillations are ignored.

|}

=== Reactive and unreactive trajectories ===

{| class="wikitable" border="1"
! p1 !! p2 !! Total Energy !! Plot of Trajectory !! Unreactive or Reactive
|-
| -1.25 || -2.5 ||-99.018 ||[[File:Smn_H2_trajectories1.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight.
|-
| -1.5 || -2.0 || -100.456 ||[[File:Smn_H2_trajectories2.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is oscillating before and after the TS.
|-
| -1.5 || -2.5 || -98.956||[[File:Smn_H2_trajectories3.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory is oscillating from the start, i.e. from the reactants.
|-
| -2.5 || -5.0 || -84.956||[[File:Smn_H2_trajectories4.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is straight before the TS but when it returns to the reactants, the molecule is vibrating - the oscillations are of high amplitude.
|-
| -2.5 || -5.2 || -83.416||[[File:Smn_H2_trajectories5.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight - the oscillations are of high amplitude.

|}

=== Transition State Theory ===

*Assumptions:
#The reactants will go through a saddle point in the potential energy surface (transition state) and proceed to the products
#The transition state will be in (quasi) equilibrium with the reactants
#

== F-H-H System ==

=== PES Inspection ===

*The H-F bond is stronger than the H2 bond due to the large electronegativity difference between H and F, which polarises the bond introducing strong ionic character.
*Therefore, the 'F + H2' reaction will be exothermic (as it includes making a strong bond and breaking a relatively weak one) and the 'H + HF' system will be endothermic (as the strong H-F bond needs to be broken).
*As 'F + H2' is higher in energy, it is closer in energy to the transition state, according to Hammond's postulate - i.e. in an exothermic reaction the transition state will resemble the reactants (energetically and structurally).
*The surface plot shows the position of the transition state (black dot) - the energy of the transition state is -103.752.

[[File:Smn_fhh_Surface_Plot_transitionstate.jpeg|thumb|center]]
*The Internuclear distance Vs time graph below shows the F-H and H-H bond lengths at the transition state; F-H=A-B= 1.810 and H-H=BC=0.745. The plot shows the transition state because they do not oscillate with time.
[[File:smn_FHH_dvt_TS.jpeg|thumb|center]]

*EA= E(TS) - E(Reactants)
**Performed an MEP with 500000 steps, with the F-H = 1.9 Å (slightly distorted from TS) and H-H= 0.74 Å. When the reactants are F and H2:
***EA = -103.752 - - 104.008 = +0.256 kcalmol-1EXO
**Performed an MEP with 500000 steps, with the F-H = 1.8 Å and H-H= 0.8 Å (slightly distorted from TS). When the reactants are H and H-F:
***EA = -103.752 - - 103.877 = -0.125 kcalmol-1 ENDO

== Reaction dynamics ==

=== Reactive trajectory of F and H-H ===
*exothermic reaction
*to conserve E, the E released is used to vibrate the F-H molecule
*check the IR frequencies of F-H and H-H ~ intensities

[[File:Smn_momentum_FHH.jpeg|thumb|center]]

*momentum vs time plot shows that H-H is constant whereas F-H has an oscillating momentum.

[[File:Smn_energy_fhh_rxndynamics.jpeg]]

=== Polanyis Rules ===
*negative momentum are unreactive
*FH = 2.1 HH= 0.74 p(FH)= -0.5 p(HH) = 0.3 - small momentum go to reaction
[[File:Smn_momentum_HH_0.3.jpeg|thumb|center]]

*FH = 2.1 HH= 0.74 p(FH)= -0.5 p(HH) = 3 - small momentum go to reaction
[[File:Smn_momentum_HH_3.jpeg|thumb|center]]

File:Smn momentum HH 3.jpeg

2018-05-18T12:58:28Z

Smn216:

MRD:saramalek

2018-05-18T12:57:14Z

Smn216: /* = */

== H + H2 system ==

=== Gradient of the potential energy surface ===

dV/dr = 0 (where r= r1 and r2 i.e. both partial derivatives = 0) at minimum points and transition structures (saddle points), as a zero gradient represents turning points. A minimum point and saddle point can be distinguished by taking the second partial derivative test; the Hessian determinant ,D, is calculated. If:
*D<0 : Saddle point.
*D>0 AND the second partial derivative is >0.

=== Locating the transition state ===

rts=r1 = r2 = 0.908 Å 

{| class="wikitable" border="1"
! Internuclear Distance VS Time Graph !! Analysis
|-
| [[File:TS_H2_distances.jpeg|thumb|center]] || The graph shows two approximately linear lines i.e. there is no/very little oscillation in energy (symmetric vibration of AB and AC)

|}

=== Reaction path ===

{| class="wikitable" border="1"
! MEP !! Dynamic !! Comparison
|-
| [[File:Rxn_path_MEP.jpeg|thumb|center]] || [[File:Reaction_path_dynamic.jpeg|thumb|center]] || The dynamic contour plot shows an oscillating trajectory as opposed to the straight trajectory in the MEP contour plot - this oscillations are due to vibrations of the molecule and there are none present in the MEP plot because it is the lowest energy path and thus oscillations are ignored.

|}

=== Reactive and unreactive trajectories ===

{| class="wikitable" border="1"
! p1 !! p2 !! Total Energy !! Plot of Trajectory !! Unreactive or Reactive
|-
| -1.25 || -2.5 ||-99.018 ||[[File:Smn_H2_trajectories1.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight.
|-
| -1.5 || -2.0 || -100.456 ||[[File:Smn_H2_trajectories2.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is oscillating before and after the TS.
|-
| -1.5 || -2.5 || -98.956||[[File:Smn_H2_trajectories3.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory is oscillating from the start, i.e. from the reactants.
|-
| -2.5 || -5.0 || -84.956||[[File:Smn_H2_trajectories4.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is straight before the TS but when it returns to the reactants, the molecule is vibrating - the oscillations are of high amplitude.
|-
| -2.5 || -5.2 || -83.416||[[File:Smn_H2_trajectories5.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight - the oscillations are of high amplitude.

|}

=== Transition State Theory ===

*Assumptions:
#The reactants will go through a saddle point in the potential energy surface (transition state) and proceed to the products
#The transition state will be in (quasi) equilibrium with the reactants
#

== F-H-H System ==

=== PES Inspection ===

*The H-F bond is stronger than the H2 bond due to the large electronegativity difference between H and F, which polarises the bond introducing strong ionic character.
*Therefore, the 'F + H2' reaction will be exothermic (as it includes making a strong bond and breaking a relatively weak one) and the 'H + HF' system will be endothermic (as the strong H-F bond needs to be broken).
*As 'F + H2' is higher in energy, it is closer in energy to the transition state, according to Hammond's postulate - i.e. in an exothermic reaction the transition state will resemble the reactants (energetically and structurally).
*The surface plot shows the position of the transition state (black dot) - the energy of the transition state is -103.752.

[[File:Smn_fhh_Surface_Plot_transitionstate.jpeg|thumb|center]]
*The Internuclear distance Vs time graph below shows the F-H and H-H bond lengths at the transition state; F-H=A-B= 1.810 and H-H=BC=0.745. The plot shows the transition state because they do not oscillate with time.
[[File:smn_FHH_dvt_TS.jpeg|thumb|center]]

*EA= E(TS) - E(Reactants)
**Performed an MEP with 500000 steps, with the F-H = 1.9 Å (slightly distorted from TS) and H-H= 0.74 Å. When the reactants are F and H2:
***EA = -103.752 - - 104.008 = +0.256 kcalmol-1EXO
**Performed an MEP with 500000 steps, with the F-H = 1.8 Å and H-H= 0.8 Å (slightly distorted from TS). When the reactants are H and H-F:
***EA = -103.752 - - 103.877 = -0.125 kcalmol-1 ENDO

== Reaction dynamics ==

=== Reactive trajectory of F and H-H ===
*exothermic reaction
*to conserve E, the E released is used to vibrate the F-H molecule
*check the IR frequencies of F-H and H-H ~ intensities

[[File:Smn_momentum_FHH.jpeg|thumb|center]]

*momentum vs time plot shows that H-H is constant whereas F-H has an oscillating momentum.

[[File:Smn_energy_fhh_rxndynamics.jpeg]]

=== Polanyis Rules ===
*negative momentum are unreactive
*FH = 2.1 HH= 0.74 p(FH)= -0.5 p(HH) = 0.3 - small momentum go to reaction
[[File:Smn_momentum_HH_0.3.jpeg|thumb|center]]

File:Smn momentum HH 0.3.jpeg

2018-05-18T12:57:09Z

Smn216:

MRD:saramalek

2018-05-18T12:45:53Z

Smn216: /* Reaction dynamics */

== H + H2 system ==

=== Gradient of the potential energy surface ===

dV/dr = 0 (where r= r1 and r2 i.e. both partial derivatives = 0) at minimum points and transition structures (saddle points), as a zero gradient represents turning points. A minimum point and saddle point can be distinguished by taking the second partial derivative test; the Hessian determinant ,D, is calculated. If:
*D<0 : Saddle point.
*D>0 AND the second partial derivative is >0.

=== Locating the transition state ===

rts=r1 = r2 = 0.908 Å 

{| class="wikitable" border="1"
! Internuclear Distance VS Time Graph !! Analysis
|-
| [[File:TS_H2_distances.jpeg|thumb|center]] || The graph shows two approximately linear lines i.e. there is no/very little oscillation in energy (symmetric vibration of AB and AC)

|}

=== Reaction path ===

{| class="wikitable" border="1"
! MEP !! Dynamic !! Comparison
|-
| [[File:Rxn_path_MEP.jpeg|thumb|center]] || [[File:Reaction_path_dynamic.jpeg|thumb|center]] || The dynamic contour plot shows an oscillating trajectory as opposed to the straight trajectory in the MEP contour plot - this oscillations are due to vibrations of the molecule and there are none present in the MEP plot because it is the lowest energy path and thus oscillations are ignored.

|}

=== Reactive and unreactive trajectories ===

{| class="wikitable" border="1"
! p1 !! p2 !! Total Energy !! Plot of Trajectory !! Unreactive or Reactive
|-
| -1.25 || -2.5 ||-99.018 ||[[File:Smn_H2_trajectories1.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight.
|-
| -1.5 || -2.0 || -100.456 ||[[File:Smn_H2_trajectories2.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is oscillating before and after the TS.
|-
| -1.5 || -2.5 || -98.956||[[File:Smn_H2_trajectories3.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory is oscillating from the start, i.e. from the reactants.
|-
| -2.5 || -5.0 || -84.956||[[File:Smn_H2_trajectories4.jpeg|thumb|center]] || UNREACTIVE - trajectory starts at the reactants but once it reaches the TS, it goes back to the reactants instead of proceeding towards the products. The trajectory is straight before the TS but when it returns to the reactants, the molecule is vibrating - the oscillations are of high amplitude.
|-
| -2.5 || -5.2 || -83.416||[[File:Smn_H2_trajectories5.jpeg|thumb|center]] || REACTIVE - trajectory starts at reactants, passes the TS and gets to the products. The trajectory starts oscillating after it passes the TS, before which it is straight - the oscillations are of high amplitude.

|}

=== Transition State Theory ===

*Assumptions:
#The reactants will go through a saddle point in the potential energy surface (transition state) and proceed to the products
#The transition state will be in (quasi) equilibrium with the reactants
#

== F-H-H System ==

=== PES Inspection ===

*The H-F bond is stronger than the H2 bond due to the large electronegativity difference between H and F, which polarises the bond introducing strong ionic character.
*Therefore, the 'F + H2' reaction will be exothermic (as it includes making a strong bond and breaking a relatively weak one) and the 'H + HF' system will be endothermic (as the strong H-F bond needs to be broken).
*As 'F + H2' is higher in energy, it is closer in energy to the transition state, according to Hammond's postulate - i.e. in an exothermic reaction the transition state will resemble the reactants (energetically and structurally).
*The surface plot shows the position of the transition state (black dot) - the energy of the transition state is -103.752.

[[File:Smn_fhh_Surface_Plot_transitionstate.jpeg|thumb|center]]
*The Internuclear distance Vs time graph below shows the F-H and H-H bond lengths at the transition state; F-H=A-B= 1.810 and H-H=BC=0.745. The plot shows the transition state because they do not oscillate with time.
[[File:smn_FHH_dvt_TS.jpeg|thumb|center]]

*EA= E(TS) - E(Reactants)
**Performed an MEP with 500000 steps, with the F-H = 1.9 Å (slightly distorted from TS) and H-H= 0.74 Å. When the reactants are F and H2:
***EA = -103.752 - - 104.008 = +0.256 kcalmol-1EXO
**Performed an MEP with 500000 steps, with the F-H = 1.8 Å and H-H= 0.8 Å (slightly distorted from TS). When the reactants are H and H-F:
***EA = -103.752 - - 103.877 = -0.125 kcalmol-1 ENDO

== Reaction dynamics ==

=== Reactive trajectory of F and H-H ===
*exothermic reaction
*to conserve E, the E released is used to vibrate the F-H molecule
*check the IR frequencies of F-H and H-H ~ intensities

[[File:Smn_momentum_FHH.jpeg|thumb|center]]

*momentum vs time plot shows that H-H is constant whereas F-H has an oscillating momentum.

[[File:Smn_energy_fhh_rxndynamics.jpeg]]

===