ChemWiki - User contributions [en]

MRD:SanzianaFoia01118973-2018

2018-05-11T17:00:07Z

Msf116: /* Reaction Dynamics */

== Exercise 1: H+H2 system ==

=== Distinguishing between transition state and minimum points ===
At a transition structure, both of the components of the gradient of the potential energy surface have values of zero (both slopes are zero). This is also the case with minimum points. Hence, only looking at the gradient (first derivative) would not give enough information to distinguish between transition states and minima.

Therefore, to distinguish between minima and transition structures we can look at the curvature (second derivative) of the potential energy surface orthogonal components. At the transition state, the curvature (second derivative) of one component is negative and the curvature of the other component is positive (in other words, a transition state point, i.e. saddle point, has a local maximum in one direction and a local minimum in another direction).

In contrast, the curvature (second derivative) for a minimum is positive in both components of the potential energy surface.

=== Estimating transition state position ===
For a symmetric system the transition state occurs at r1= r2=rts. The best estimate of the transition state position for the H+H2 system was found at rts = 0.908 Å. At this position, no oscillations were observed in on the internuclear distance vs time plot, suggesting that the system was at equilibrium and hence confirming that the position corresponded to the transition state. Moreover, the plot shows that A-B and B-C bond distances are not changing over time at pAB=pBC=0, therefore confirming that the state observed, i.e. transition state, is at equilibrium.

[[ File:Q2 InternuclearDistanceVSTime plot TS MEP 01118973.png | 400px | caption ]]

=== Reactive and unreactive trajectories ===
{| class="wikitable"
!p1
!p2
!Total Energy/kcal mol-1
!Reactive?
!Description
!Contour Plot
|-
|<nowiki>-1.25</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-99.018</nowiki>
|YES
|The reaction path goes all the way from the reactants' channel to the products' channel. No vibrations are observed in the reactants but oscillations can be seen in the products.
|
[[ File:Q4 1 contour01118973.png | 400px | caption ]]

|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.0</nowiki>
|<nowiki>-100.456</nowiki>
|NO
|The reaction path begins in the reactants' channel, approaches (but does not reach) the transition state and also ends in the reactants' channel as the activation energy of the reaction is not reached. The wavy line suggests that the initial molecule is oscillating.
|
[[ File:Q4 2 contour01118973.png | 400px | caption ]]
|-
|<nowiki>-1.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-98.956</nowiki>
|YES
|The trajectory is reactive (similar to first trajectory). Molecule vibrates both in the reactants and in the products' channel.
|
[[ File:Q4 3 contour01118973.png | 400px | caption ]]
|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.0</nowiki>
|<nowiki>-84.956</nowiki>
|NO
|The path starts in the reactants' channel and nearly reaches the transition state, however as it does not overcome the transition state energy, it does not react the products' channel.
|
[[ File:Q4 4 contour01118973.png | 400px | caption ]]
|-
|<nowiki>-2.5</nowiki>
|<nowiki>-5.2</nowiki>
|<nowiki>-83.416</nowiki>
|YES
|The trajectory starts in the reactants' channel, the activation energy is reached and the system reaches into the products' channel.
|
[[ File:Q4 5 contour01118973.png | 400px | caption ]]
|}

=== Assumptions of Transition State Theory ===
Transition State Theory explains the molecular reaction dynamics by assuming a metastable equilibrium is established between the reactants and the transition state.
* All energies of the reactant atoms are following the Boltzmann distribution - this is only true when systems have enough time to reach a thermal equilibrium.
* Born-Oppenheimer approximation - the nuclei are considered to be much heavier than the electrons, therefore electrons can be negligible, and the particles are assumed to obey classical mechanics. This means that the transition state is only reached if the particles have enough energy,
* Every reaction passes through the the transition state - not always the case at high temperatures.

== Exercise 2: the F-H-H system ==

=== F+H2 and H+HF reactions ===
F+H2 is exothermic whilst H+HF is endothermic. This can be best illustrated using a surface energy plot. For the first reaction (please see figure below), the reactants are at a higher energy than the products (the products' channel is at a lower energy than that of the reactants), hence the energy change from reactants to products is negative, i.e. exothermic. For the reverse reaction, the the reactants are found at a lower energy hence the reaction is endothermic. This is in accordance with bond strengths (F-H bond is very strong and will readily form, hence the exothermic reaction whilst breaking a F-H bond to form is H-H requires an energy input, therefore the endothermic reaction).<gallery>
File:Surface Plot endoexo.png
</gallery>

=== Locating the transition state ===
The transition state was found at positions rAB=1.811 and rBC=0.744 , where (A, B and C are F, H and H respectively). The energy corresponding to the transition state was found as E=-103.752. <gallery>
File:TSFcontour.png
</gallery><gallery>
File:TSFdist.png
</gallery>

=== Activating energies for the F+H2 and H+HF reactions ===
The activation energy was computed using coordinates slightly displaced from the transition state and using the MEP calculation type at 20000 steps so that the last geometry corresponded to the products of each reaction in turn. Using this method, the activation energy for F+H2 was found to be Ea=0.161 whereas the activation energy for H+HF was found as Ea=30.153.

=== Reaction Dynamics ===
Reaction conditions for a reactive pathway for the F-H-H system: ''rAB=0.74, rBC=2.1, pAB=-1.0, pBC=-1.5. ''<gallery>
File:Reactiiiii01118973iSanzianaiive.png
</gallery><gallery>
File:Reactive 01118973.png
</gallery>At the start, the H-H molecule vibrates whereas F does not. After the collision, the H-F molecule is formed and oscillates strongly. The energy released in the reaction will be converted from potential energy into kinetic energy. IR spectroscopy could be used for experimental confirmation.

MRD:SanzianaFoia01118973-2018

MRD:SanzianaFoia01118973-2018

2018-05-10T14:29:47Z

Msf116: /* 4. 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 happ */

== 1. 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. ==

At a minimum,

At a transition structure, the orthogonal components of the gradient of the potential energy surface have values of zero as the slope of each component is zero (characteristic to saddle point).

Distinguishing minima and transition states using curvature: at the transition state, the curvature (second derivative) is negative whilst the curvature (second derivative) for a minimum is positive.

== 2. Report your best estimate of the transition state position (rts) and explain your reasoning illustrating it with a "Internuclear Distances vs Time" plot for a relevant trajectory. ==
The best estimate of the transition state position was found using an Internuclear Distances vs Time plot and was found as rts = 0.908 Å.

[[ File:Q2 InternuclearDistanceVSTime plot TS MEP 01118973.png | 400px | caption ]]

== 4. 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. ==
{| class="wikitable"
!Set Number
!p1
!p2
!Total Energy/kcal mol-1
!Reactive?
!Description
|-
|1
|<nowiki>-1.25</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-99.018</nowiki>
|YES
|
|-
|2
|<nowiki>-1.5</nowiki>
|<nowiki>-2.0</nowiki>
|<nowiki>-100.456</nowiki>
|NO
|
|-
|3
|<nowiki>-1.5</nowiki>
|<nowiki>-2.5</nowiki>
|<nowiki>-98.956</nowiki>
|YES
|
|-
|4
|<nowiki>-2.5</nowiki>
|<nowiki>-5.0</nowiki>
|<nowiki>-84.956</nowiki>
|NO
|
|-
|5
|<nowiki>-2.5</nowiki>
|<nowiki>-5.2</nowiki>
|<nowiki>-83.416</nowiki>
|YES
|
|}

MRD:SanzianaFoia01118973-2018

2018-05-10T14:25:52Z

Msf116:

MRD:SanzianaFoia01118973-2018

2018-05-10T14:24:27Z

Msf116:

MRD:SanzianaFoia01118973-2018

2018-05-10T14:23:46Z

Msf116:

File:Q2 InternuclearDistanceVSTime plot TS MEP 01118973.png

2018-05-10T14:20:31Z

Msf116:

MRD:SanzianaFoia01118973-2018

2018-05-10T14:17:45Z

2017-03-24T17:32:16Z

Msf116:

== '''NH3 molecule''' ==

==== Summary of Results ====
* N-H bond distance = 1.018 Å

* H-N-H bond angle = 105.74°
* Molecule name: Ammonia
* Calculation method: RB3LYP
* Basis set: 6-31G(d,p)
* Final energy E(RB3LYP) in atomic units: -56.55776873 au
* RMS Gradient Norm: 0.00000485 au
* Point group of molecule: C3V

<jmol><jmolApplet>
<title>Figure 1. Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SANZIANAFOIA_NH3_OPTF_POP_1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

The experimentally determined value of the N-H bond in ammonia is 1.012 Å, which is comparable to the computed value in this report. Moreover, the H-N-H bond angle as per literature is 106.67°, which is close to the computerised value determined here.<ref name="Millsian" />

<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>

Gaussview performs optimisations of molecules by finding the optimum bond lengths and angles that would result in no overall force in the molecule, as well as yield the lowest possible energy and hence the most stable and most likely conformation of the molecule. Gaussview initiates the optimisation process using the input bond length value declared (or set by the software by default) and reccurently varies the distance between nuclei until the potential energy reaches a minimum. This corresponds to the equilibrium positions of the atoms in the bond. To assess whether the optimisation has reached completion it is necessary to verify whether the maximum force (table above) is close to zero, as this suggests that the system is at its most stable state.

The output text file for the optimised molecule can be found [[Media:SANZIANAFOIA_NH3_OPTF_POP_1.LOG|here]].

==== Frequency Analysis ====
[[File:SanzianaFoia_NH3_Display_Vibrations.jpg|thumb|Figure 2. Vibrational frequencies of NH3|none]]

The 3N-6 rule dictates that any molecule with N atoms will have 3N-6 vibrational modes. The ammonia molecule (which has four atoms), wold therefore be expected to have 3*4-6 = 6 normal modes of vibration. Out of these, modes 2,3 (vibrational frequency 1693.95) are degenerate and 5,6 (vibrational frequency 3589.82) respectively. Mode numbers 1,2,3 (vibrational frequences 1089.54, 1693.95, 1693.95) are bending vibrations whilst modes 4,5,6 are bond-stretch vibrations. The mode that is highly symmetric is vibration number 1, i.e. frequency 1089.54). Moreover, bending vibrational mode 1 is also called the <nowiki>''umbrella''</nowiki> mode. The experimental spectrum of ammonia would only display two bands. These are represented by the infrared amplitudes on 145.3814 (vibrational mode 1) and 13.5533 (vibrational modes 2 and 3, which are degenerate and therefore appear on the spectrum as a single band).

Vibrational frequency is related to the second order derivative of the potential energy vs internuclear distance plot. Therefore, negative frequencies suggest either the presence of a maximum or a concave curve, hence showing that the system has not reached the minimum of the potential well. Consequently, this infers that the molecule was not successfully optimised. The fact that all the frequencies displayed are positive values reinforces that the optimisation of the molecule reached completion.

==== Charge analysis ====

Charge on the N-atom: -1.125

Charge on the H-atom: +0.375

The expected charge for the nitrogen atom is negative whereas the charge of the hydrogen atom should be positive due to the electronegativity difference between the two atoms, i.e. . This implies that the N atom would have a higher affinity for electrons, hence rendering its partially negative charge and H its partially positive charge.

=== '''N2''' ===

==== Summary of Results ====
* N-N bond distance = 1.106 Å
* Molecule name: Nitrogen
* Calculation method: RB3LYP
* Basis set: 6-31G(d,p)
* Final energy E(RB3LYP) in atomic units (au): -109.52412868
* RMS Gradient Norm: 0.00000015 au
* Point group of molecule: D∞

<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 0.000000 0.001200 YES
</pre>

The output text file for the optimised N2 molecule can be found [[Media:SANZIANAFOIA_N2_OPTF_POP_5.LOG|here]].

==== Frequency Analysis ====
[[File:SanzianaFoia N2 Display Vibrations.jpg|thumb|Figure 3. Vibrational frequency of N2|none]]

=== '''H2''' ===

==== Summary of Results ====
* H-H bond distance = 0.743 Å
* Molecule name: Hydrogen
* Calculation method: RB3LYP
* Basis set: 6-31G(d,p)
* Final energy E(RB3LYP) in atomic units (au): -1.17853930
* RMS Gradient Norm: 0.00012170 au
* Point group of molecule: D∞

<pre>
Item Value Threshold Converged?
Maximum Force 0.000211 0.000450 YES
RMS Force 0.000211 0.000300 YES
Maximum Displacement 0.000278 0.001800 YES
RMS Displacement 0.000393 0.001200 YES
</pre>

The output text file for the optimised H2 molecule can be found [[Media:SANZIANAFOIA_H2_OPTF_POP_1.LOG|here]].

==== Frequency Analysis ====
[[File:SanzianaFoia_H2_Display_Vibrations.jpg|thumb|Figure 4. Vibrational frequency of H2|none]]

=== '''Determination of energy change of reaction N2 + 3H2 -> 2NH3''' ===
E(NH3)= -56.55776873 au

2*E(NH3)= -113.11553746 au

E(N2)= -109.52412868 au

E(H2)= -1.17853930 au

3*E(H2)= -3.5356179 au

ΔE = 2*E(NH3)-[E(N2)+3*E(H2)] = -113.11553746 - (-109.52412868 - 3.5356179) = -0.05579088 au

ΔE = 2625.5*(-0.05579088) = -146.4789554 kJ/mol

The ammonia product is more stable. The reaction is exothermic hence energy is released when the gases react together, making ammonia more thermodynamically favourable.

== '''Project molecule: ClF3 ''' ==
=== '''Summary of results '''===
* Cl-Faxial bond distance = 1.729 Å
* Cl-Fequatorial bond distance = 1.651 Å
* Faxial-Cl-Fequatorial bond angle = 87.14°
* Faxial-Cl-Faxial bond angle = 174.3°
* Molecule name: Chlorine trifluoride
* Calculation method: RB3LYP
* Basis set: 6-31G(d,p)
* Final energy E(RB3LYP) in atomic units: -759.46531688 au
* RMS Gradient Norm: 0.00002465 au
* Point group of molecule: C2V

<jmol><jmolApplet>
<title>Figure 5. Chlorine trifluoride</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SANZIANAFOIA_CLF3_OPTF_POP_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

The literature found values for the axial fluorine - chlorine and the equatorial fluorine - chlorine bonds are 1.698 and 1.598 respectively. Moreover, the Faxial-Cl-Fequatorial bond angle was found to be 87.48, which is comparable to the computed value displayed in this report.<ref name="Smith" />
<pre>
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000204 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
</pre>

As per the ''Item'' table presented above, the maximum force in the optimised molecule is close to zero. This suggests that the optimisation process went to completion as the atoms in the molecule are at their equilibrium state.

The output text file for the optimised ClF3 molecule can be found [[Media:SANZIANAFOIA_CLF3_OPTF_POP_2.LOG|here]].

=== '''Frequency analysis '''===

[[File:SanzianaFoia_clf3_Display_Vibrations.jpg|thumb|Figure 6. Vibrational frequencies of ClF3|none]]

==='''Charge analysis'''===

Charge on the Cl-atom: +1.225

Charge on the equatorial F-atom: -0.316

Charge on the axial F-atom: -0.454

Write a sentence saying what charge (positive or negative) you would expect for N and H and why

===''' Molecular Orbitals of ClF3 '''===
The MO presented in Figure 7 is a bonding molecular orbital formed from s AOs from the chlorine and the three fluorine atoms. It is occupied by a pair of spin-opposed electrons and it is relatively high in energy compared to lower-lying orbitals, such as the non-bonding MOs coming from 1s atomic orbitals of the three atoms in the molecule. The MO displayed above would be lower in energy than its component atomic orbitals, hence contributing to the stability of the molecule and to bonding.

[[File:SanzianaFoia_MO9_1.jpg|281x281px|thumb|Figure 7. Sigma bonding MO in ClF3|none]]

Figure 8 depicts a MO consisting of a mixture of both bonding and antibonding MOs. s orbitals from the axial fluorine atoms and the chlorine form bonding interactions whereas s orbitals from the equatorial fluorine and the chlorine respectively contribute to a molecular antibonding interaction. The molecular orbital showed in the figure is moderately high in energy and is fully occupied. The bonding interaction encompassed by the MO presented would contribute to the bonding of molecule whereas the antibonding interaction would contribute to the breakdown of the Cl-Fequatorial bond.

[[File:SanzianaFoia_MO10_2.jpg|281x281px|thumb|Figure 8. Mixed sigma bonding and antibonding MO in ClF3|none]]

The AOs that contribute to the formation of the molecular orbital presented in the figure below are s orbitals on the Cl and F atoms. The MO shown is fully occupied and of antibonding type, being relatively high in energy. The overall effect of this σ* orbital would be towards the breaking of all the bonds comprised in the molecule.

[[File:SanzianaFoia_MO12_3.jpg|281x281px|thumb|Figure 9. Sigma antibonding MO in ClF3|none]]

Figure 10 shows a π (bonding) orbital formed by the p orbitals on all the component atoms in the considered molecule. The MO is shallow in energy, suggesting that the position of its electron cloud is further away from the nuclei compared to deeper in energy orbitals, like the one depicted in Figure 2. The molecular orbital is fully occupied and its effect would be to contribute to the lowering in energy and bonding state of the molecule.

[[File:SanzianaFoia_MO15_4.jpg|281x281px|thumb|Figure 10. Pi bonding MO in ClF3|none]]

Figure 11 below displays the π* (antibonding) orbital comprised from p orbitals on Cl and the three F atoms in the molecule. The MO orbital presented here is the HOMO (highest occupied molecular orbital) of the molecule, and it contains two spin-paired electrons. The effect of this molecular orbital would be to increase the energy of the molecule, hence decreasing its stability and raising its likelihood to break down.

[[File:SanzianaFoia_MO22_5.jpg|281x281px|thumb|Figure 11. Pi antibonding MO in ClF3|none]]

=== '''F2''' ===
==== Summary of Results ====
* F-F bond distance = 1.403 Å
* Molecule name: Fluorine
* Calculation method: RB3LYP
* Basis set: 6-31G(d,p)
* Final energy E(RB3LYP) in atomic units: -199.49825218 au
* RMS Gradient Norm: 0.00007365 au
* Point group of molecule: D∞

<jmol><jmolApplet>
<title>Figure 12. Fluorine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SANZIANAFOIA_F2_OPTF_POP_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000128 0.000450 YES
RMS Force 0.000128 0.000300 YES
Maximum Displacement 0.000156 0.001800 YES
RMS Displacement 0.000221 0.001200 YES

</pre>

The output text file for the optimised F2 molecule can be found [[Media:SANZIANAFOIA_F2_OPTF_POP_1.LOG|here]].

==== Frequency Analysis ====
[[File:SanzianaFoia_F2_Display_Vibrations.jpg|thumb|Figure 13. Vibrational frequency of F2|none]]

==== Charge analysis ====

Charge on the F-atoms: 0.000

=== '''Cl2''' ===
==== Summary of Results ====
* Cl-Cl bond distance = 2.042 Å
* Molecule name: Chlorine
* Calculation method: RB3LYP
* Basis set: 6-31G(d,p)
* Final energy E(RB3LYP) in atomic units: -920.34987886 au
* RMS Gradient Norm: 0.00002511 au
* Point group of molecule: D∞

<pre>
Item Value Threshold Converged?
Maximum Force 0.000043 0.000450 YES
RMS Force 0.000043 0.000300 YES
Maximum Displacement 0.000121 0.001800 YES
RMS Displacement 0.000172 0.001200 YES
</pre>

The output text file for the optimised Cl2 molecule can be found [[Media:SANZIANAFOIA_Cl2_OPTF_POP_1.LOG|here]].

==== Frequency Analysis ====
[[File:SanzianaFoia_cl2_Display_Vibrations.jpg|thumb|Figure 14. Vibrational frequencies of Cl2|none]]

==== Charge analysis ====

Charge on the Cl-atoms: 0.000

==='''Determination of energy change of reaction 3F2 + Cl2->2ClF3 '''===

E(ClF3)= -759.46531688 au

2*E(ClF3)= -1518.930634 au

E(F2)= -199.49825218 au

E(Cl2)= -920.34987886 au

3*E(F2)= -598.4947565 au

ΔE = 2*E(ClF3)-[E(Cl2)+3*E(F2)] = -1518.930634 - (-920.34987886 - 598.4947565) = -0.0859984 au

ΔE = -225.7887992 kJ/mol

The chlorine trifluoride product is more stable than the reactants. The formation ClF3 of is exothermic. Therefore, the energy of the system is lowered as the reaction progresses, making ClF3 the thermodynamical product of the reaction.
== '''References''' ==
<references>
<ref name="Millsian">2. Summary Tables of Calculated and Experimental Parameters of Diatomic, Triatomic, Organic, Silicon, Boron, Aluminium and Organometallic Molecules, Exemplary Results on Condensed Matter Physics, One-Through Twenty-Electron Atoms, Excited States of Helium, g Factor, and Fundamental Particle Masses [Internet]. Millsian. 2017 [cited 24 March 2017]. Available from: http://www.millsian.com/summarytables/SummaryTables022709S.pdf</ref>
<ref name="Smith">Smith D. The Microwave Spectrum and Structure of Chlorine Trifluoride. The Journal of Chemical Physics. 1953;21(4):609-614.</ref>
</references>