== Exercise 1 ==
=== 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? ===

The transition state is located at the maximum on the potential energy surface. At this point, the gradient of the potential(∂V(ri)/∂ri) is zero.

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

The transition state position (rts) is at 90.8 pm. It can be seen in the image that if the initial r1 and r2 are set at 90.8 pm, the distance remains constant. This means the system is at the transition state since it doesn't undergo any periodic vibration.

.
[[File:ns618.jpeg]]

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

On the dynamics trajectory, it is seen that after the molecule BC is formed, it undergoes vibrational motion as it moves away from A. However, this cannot be seen in the mep trajectory

[[File:ns618k.jpeg]]
mep trajectory

[[File:ns618l.jpeg]]
dynamcis trajectory

===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
! p1/ g.mol-1.pm.fs-1 !! p2/ g.mol-1.pm.fs-1 !! Etot !! Reactive? !! Description of the dynamics !! Illustration of the trajectory
|-
| -2.56 || -5.1 || -414.28 || yes || A collides with BC and forms the molecule AB. C then moves away from AB || [[File:ns618a.jpeg]]
|-
| -3.1 || -4.1 || -420.077 || no || A moves towards BC, but doesnt collide with it. It then moves away from BC || [[File:ns618b.jpeg]]
|-
| -3.1 || -5.1 || -413.977 || yes || A collides with BC and forms the molecule AB. C then moves away from AB || [[File:ns618c.jpeg]]
|-
| -5.1 || -10.1 || -357.277 || yes || A collides with BC and forms the molecule AB. C moves away from AB, and then moves back towards AB. C collides with AB and forms BC. A then moves away from BC. || [[File:ns618d.jpeg]]
|-
| -5.1 || -10.6 || -349.477 || yes || A collides with BC and forms the molecule AB. C moves away from AB, and then moves back towards AB. C collides with AB and forms BC. A moves away from BC and then moves back toward BC. A collides with BC and forms AB. C then moves away from AB. || [[File:ns618e.jpeg]]
|-
|}

===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 the potential energy surface of F + H2, it is seen that the energy of the reactant is higher than that of the product. Hence, it is an exothermic reaction. The reverse reaction, H + HF, is an endothermic reaction. The bond strength of HF is greater than that of HH. Hence, HF is at a lower energy than HH.
[[File:ns618g.jpeg]]

===Locate the approximate position of the transition state===

At the transition state, rab = 180pm and rbc = 74.5pm. In the figure, AB is FH and BC is HH.

[[File:ns618f.jpeg]]

===Report the activation energy for both reactions===

Activation energy of F + H2 = 104.95kj/mol.

[[File:ns618h.jpeg]]

Activation energy of H + HF = 291.185kj/mol.

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

The F atom collides with the H2 molecule and forms the HF molecule. When the HF is formed, it gains kinetic energy. This energy results in the molecule moving from the molecular ground state to a vibrational excited state. The molecule then moves back to the ground state. Some of the energy is emitted in the form of radiation, resulting in the lowering of the total energy. This can be confirmed using IR spectroscopy. The intensity of the peak in the absorbtion spectrum will be lower than the intensity of the peak in the emission spectrum.

[[File:ns618i.jpeg]]

===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.===

Higher vibrational energy leads to more efficient endothermic reaction. THis is beacuase if there was a high translational energy, the atom would collide with the molecule and then return in the opposite direction. Also, the direction of the vibrational motion aligns with the direction that fvours the formation of the product.
Higher translational energy leads to a more efficient exothermic reaction. This is because higher vibration makes it harder to cross the barrier since the product is at a lower energy. The system will move up the vallet and form the reactants once again.

File:Ns618l.jpeg

2020-05-22T20:53:19Z

Ns618:

MRD:01567335

2020-05-21T17:29:24Z

Ns618: /* Exercise 1 */

MRD:01567335

2020-05-21T12:17:56Z

Ns618:

MRD:01567335

2020-05-21T12:11:06Z

Ns618:

MRD:01567335

2020-05-21T12:06:46Z

Ns618: Created page with "== Exercise 1 =="

== Exercise 1 ==

2019-03-15T12:11:58Z

Ns618:

'''Optimzed NH3'''
<pre>

Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000072 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
Predicted change in Energy=-5.986278D-10
Optimization completed.
-- Stationary point found.</pre>
{| class="wikitable"
|'''Molecule'''
|NH3
|-
|'''Calculation Method'''
|RB3LYP
|-
|'''Basis Set'''
|6-31G(d,p)
|-
|'''Final Energy E(RB3LYP)'''
|<nowiki>-56.55776873 a.u.</nowiki>
|-
|'''RMS Gradient'''
|0.00000485 a.u.
|-
|'''Point Group'''
|C3V
|}
N-H Bond Length : 1.01798 angstrom

H-N-H Bond Angle : 105.741 degrees

<jmol><jmolApplet>
<title>optimized NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NS618 NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:Vibration display.png]]

{| class="wikitable"
|'''Wavenumber (/cm)'''
|1089.5366
|1693.9474
|-
|'''Symmetry'''
|A1
|E
|-
|'''intensity (arbitrary units)'''
|145.3814
|13.5533
|-
|}

<pre>
Charge on N-atom = -1.125
Charge on H-atom = +0.375

Expected charge on N-atom is -3 and on H-atom is +1
</pre>
'''Optimzed H2'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-1.164080D-13
Optimization completed.
-- Stationary point found.
</pre>
{| class="wikitable"
|'''Molecule'''
|H2
|-
|'''Calculation Method'''
|RB3LYP
|-
|'''Basis Set'''
|6-31G(d,p)
|-
|'''Final Energy E(RB3LYP)'''
|<nowiki>-1.17853936 a.u.</nowiki>
|-
|'''RMS Gradient'''
|0.00000017 a.u.
|-
|'''Point Group'''
|D*H
|}

H-H Bond Length : 0.74279 angstrom

<jmol><jmolApplet>
<title>optimized NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NS618 H2 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:Vibration display2.png]]

{| class="wikitable"
|'''Wavenumber (/cm)'''
|4465.6824
|-
|'''Symmetry'''
|SGG
|-
|'''intensity (arbitrary units)'''
|0
|-
|}

<pre>
Charge on H-atom = 0

Expected charge on H-atom is 0
</pre>

'''Optimzed N2'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000000 0.001800 YES
RMS Displacement 0.000000 0.001200 YES
Predicted change in Energy=-3.383850D-13
Optimization completed.
-- Stationary point found.

</pre>
{| class="wikitable"
|'''Molecule'''
|N2
|-
|'''Calculation Method'''
|RB3LYP
|-
|'''Basis Set'''
|6-31G(d,p)
|-
|'''Final Energy E(RB3LYP)'''
|<nowiki>-109.52412868 a.u.</nowiki>
|-
|'''RMS Gradient'''
|0.00000060 a.u.
|-
|'''Point Group'''
|D*H
|}

H-H Bond Length : 1.10550 angstrom

<jmol><jmolApplet>
<title>optimized NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NS618 N26 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:Vibration display3.png]]

{| class="wikitable"
|'''Wavenumber (/cm)'''
|2457.3283
|-
|'''Symmetry'''
|SGG
|-
|'''intensity (arbitrary units)'''
|0
|-
|}

<pre>
Charge on N-atom = 0

Expected charge on N-atom is 0
</pre>

'''Optimzed P4'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000013 0.001200 YES
Predicted change in Energy=-4.333417D-11
Optimization completed.
-- Stationary point found.
</pre>
{| class="wikitable"
|'''Molecule'''
|P4
|-
|'''Calculation Method'''
|RB3LYP
|-
|'''Basis Set'''
|6-31G(d,p)
|-
|'''Final Energy E(RB3LYP)'''
|<nowiki>-1365.33522654 a.u.</nowiki>
|-
|'''RMS Gradient'''
|0.00000144 a.u.
|-
|'''Point Group'''
|C1
|}

P-P Bond Length : 1.95272, 2.18213, 2.10909 angstrom

P-P-P Bond Angle : 151.102, 61.101, 57.797 degrees

<jmol><jmolApplet>
<title>optimized NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NS618 P4 OPTF.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:Vibration display4.png]]

{| class="wikitable"
|'''Wavenumber (/cm)'''
|2457.3283
|-
|'''Symmetry'''
|SGG
|-
|'''intensity (arbitrary units)'''
|0
|-
|}

<pre>
Charge on N-atom = 0

Expected charge on N-atom is 0
</pre>