https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&feedformat=atom&user=Ri3717ChemWiki - User contributions [en]2026-04-11T00:05:23ZUser contributionsMediaWiki 1.43.0https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=790680MRD:ri3717 summer 20192019-05-23T14:36:06Z<p>Ri3717: /* 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. */</p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions #1<br />
</gallery><gallery>ri3717tableplot2.png|Initial conditions #2<br />
</gallery><gallery>ri3717tableplot3.png|Initial conditions #3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions #4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions #5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- the reactants and the transition state are in equilibrium<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
The transition state theory predictions for reaction rate values ignores the fact that the reaction may not proceed even with energy higher than the activation energy. For example, with initial conditions #4 discussed previously, the reactants approach each other with enough energy and reacts, but the product forms back the reactant species, so there is no reaction overall. This means that the transition state theory predicts reaction rate to be faster than the experimental rate.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is stronger (bond strength~ 565 kJ/mol<ref name=":0">Yoder, Claude. “Wired Chemist.” ''Common Bond Energies (D) and Bond Length (r)'', www.wiredchemist.com/chemistry/data/bond_energies_lengths.html.</ref>) than H-H bond (bond strength~ 432 kJ/mol<ref name=":0" />) because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals. H-F is highly polar while H-H bond is purely covalent. This means that the formation of H-F bond is favourable in the reaction F + H<sub>2</sub> even with the need to break the H-H bond and thus exothermic, while for the reverse reaction of H + HF, the breaking of H-F to make H-H bond is overall not stabilising and thus the reaction is endothermic. <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
=== 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. ===<br />
Initial conditions #1: r<sub>FH</sub> = 0.92, r<sub>HH</sub> = 1.5 and p<sub>FH</sub> = -0.1, p<sub>HH</sub> = -2.5<br />
<br />
I have set the initial conditions at the bottom of the entry channel (H + HF reactant conditions) with very low p<sub>FH</sub>, and obtained a reactive trajectory by decreasing p<sub>HH</sub> and increasing p<sub>FH</sub>, which is: <br />
<br />
Initial conditions #2: r<sub>FH</sub> = 0.92, r<sub>HH</sub> = 1.5 and p<sub>FH</sub> = -10.0, p<sub>HH</sub> = -1.0 <gallery><br />
Screen_Shot_2019-05-23_at_14.41.03.png|Initial conditions (F-H, H)<br />
</gallery><gallery><br />
Screen_Shot_2019-05-23_at_14.40.57.png|After reaction (F, H-H)<br />
</gallery><gallery><br />
Screen_Shot_2019-05-23_at_14.39.12.png|Contour plot for the reaction between F-H and H, producing F and H-H<br />
</gallery><gallery><br />
Screen_Shot_2019-05-23_at_14.38.15.png|Change in internuclear distances during and after reaction<br />
</gallery>For a given amount of total energy, the distribution of energy between different modes can affect the efficiency of the reaction. For example, even with enough total energy to overcome the energy barrier for the reaction to occur, if there is not enough translational energy, the reactants will not come close enough to react. <br />
<br />
The Polanyi's empirical rules state that in simple terms, translational energy is more effective in activating the reactants for exothermic reactions, while vibrational energy is more effective for endothermic reactions<ref>Bowman, Joel M. “Dynamics of the Reaction of Methane with Chlorine Atom on an Accurate Potential Energy Surface.” ''Science'', American Association for the Advancement of Science, 21 Oct. 2011, science.sciencemag.org/content/334/6054/343.</ref>. The relationship can also be shown as below: <br />
<br />
Ea = mΔH + constant <br />
<br />
where Ea= activation energy, m= indicative of the position of transition state on the reaction coordinate<ref>Wubbels, Gene G. “The Bell–Evans–Polanyi Principle and the Regioselectivity of Electrophilic Aromatic Substitution Reactions.” ''Tetrahedron Letters'', vol. 56, no. 13, 2015, pp. 1716–1719., doi:10.1016/j.tetlet.2015.02.070.</ref>. The position of the transition state is important because it determines which of the two modes, the translational energy or the vibrational energy has a larger influence on the efficiency of the reaction. <br />
<br />
Looking at initial conditions #1 ( r<sub>FH</sub> = 0.92, r<sub>HH</sub> = 1.5 and p<sub>FH</sub> = -0.1, p<sub>HH</sub> = -2.5 ) in which the reaction did not take place, we can say based on the Polanyi's rules that since this is an endothermic reaction (H + H-F --> H-H + F), vibrational energy has a more significant impact on the reaction efficiency. the momentum in F-H bond is set very low at -0.1, and this is why the reaction does not take place in these conditions. <br />
<br />
Now looking at initial conditions #2 ( r<sub>FH</sub> = 0.92, r<sub>HH</sub> = 1.5 and p<sub>FH</sub> = -10.0, p<sub>HH</sub> = -1.0 ), the reaction was successful and we can see why based on the Polanyi's rules. In initial conditions #2, the momentum in F-H bond is now set very high at -10.0, which provided the reactants with enough vibrational energy to react. <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Screen_Shot_2019-05-23_at_14.38.15.png&diff=790277File:Screen Shot 2019-05-23 at 14.38.15.png2019-05-23T13:45:17Z<p>Ri3717: </p>
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<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Screen_Shot_2019-05-23_at_14.39.12.png&diff=790269File:Screen Shot 2019-05-23 at 14.39.12.png2019-05-23T13:44:14Z<p>Ri3717: </p>
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<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Screen_Shot_2019-05-23_at_14.40.57.png&diff=790265File:Screen Shot 2019-05-23 at 14.40.57.png2019-05-23T13:43:30Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Screen_Shot_2019-05-23_at_14.41.03.png&diff=790260File:Screen Shot 2019-05-23 at 14.41.03.png2019-05-23T13:42:33Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=790065MRD:ri3717 summer 20192019-05-23T13:17:45Z<p>Ri3717: /* Report your best estimate of the transition state position (rts) for trajectories from r1 = r2 and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. */</p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions #1<br />
</gallery><gallery>ri3717tableplot2.png|Initial conditions #2<br />
</gallery><gallery>ri3717tableplot3.png|Initial conditions #3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions #4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions #5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- the reactants and the transition state are in equilibrium<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
The transition state theory predictions for reaction rate values ignores the fact that the reaction may not proceed even with energy higher than the activation energy. For example, with initial conditions #4 discussed previously, the reactants approach each other with enough energy and reacts, but the product forms back the reactant species, so there is no reaction overall. This means that the transition state theory predicts reaction rate to be faster than the experimental rate.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is stronger (bond strength~ 565 kJ/mol<ref name=":0">Yoder, Claude. “Wired Chemist.” ''Common Bond Energies (D) and Bond Length (r)'', www.wiredchemist.com/chemistry/data/bond_energies_lengths.html.</ref>) than H-H bond (bond strength~ 432 kJ/mol<ref name=":0" />) because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals. H-F is highly polar while H-H bond is purely covalent. This means that the formation of H-F bond is favourable in the reaction F + H<sub>2</sub> even with the need to break the H-H bond and thus exothermic, while for the reverse reaction of H + HF, the breaking of H-F to make H-H bond is overall not stabilising and thus the reaction is endothermic. <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy).<br />
<br />
Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) The cases studied are an illustration of Polanyi's empirical rules. <br />
<br />
=== 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. ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = 0.1, p<sub>HH</sub> = -2.5<br />
<br />
I have set the initial conditions at the bottom of the entry channel ) with very low p<sub>FH</sub>, and obrained a reactive trajectory by decreasing p<sub>HH</sub>. <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=790056MRD:ri3717 summer 20192019-05-23T13:16:55Z<p>Ri3717: /* 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. */</p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions #1<br />
</gallery><gallery>ri3717tableplot2.png|Initial conditions #2<br />
</gallery><gallery>ri3717tableplot3.png|Initial conditions #3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions #4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions #5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- the reactants and the transition state are in equilibrium<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
The transition state theory predictions for reaction rate values ignores the fact that the reaction may not proceed even with energy higher than the activation energy. For example, with initial conditions #4 discussed previously, the reactants approach each other with enough energy and reacts, but the product forms back the reactant species, so there is no reaction overall. This means that the transition state theory predicts reaction rate to be faster than the experimental rate.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is stronger (bond strength~ 565 kJ/mol<ref name=":0">Yoder, Claude. “Wired Chemist.” ''Common Bond Energies (D) and Bond Length (r)'', www.wiredchemist.com/chemistry/data/bond_energies_lengths.html.</ref>) than H-H bond (bond strength~ 432 kJ/mol<ref name=":0" />) because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals. H-F is highly polar while H-H bond is purely covalent. This means that the formation of H-F bond is favourable in the reaction F + H<sub>2</sub> even with the need to break the H-H bond and thus exothermic, while for the reverse reaction of H + HF, the breaking of H-F to make H-H bond is overall not stabilising and thus the reaction is endothermic. <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy).<br />
<br />
Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) The cases studied are an illustration of Polanyi's empirical rules. <br />
<br />
=== 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. ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = 0.1, p<sub>HH</sub> = -2.5<br />
<br />
I have set the initial conditions at the bottom of the entry channel ) with very low p<sub>FH</sub>, and obrained a reactive trajectory by decreasing p<sub>HH</sub>. <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=789980MRD:ri3717 summer 20192019-05-23T13:08:23Z<p>Ri3717: /* 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? */</p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
ADDITIONAL----------------------------------------------------<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions #1<br />
</gallery><gallery>ri3717tableplot2.png|Initial conditions #2<br />
</gallery><gallery>ri3717tableplot3.png|Initial conditions #3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions #4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions #5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- the reactants and the transition state are in equilibrium<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
The transition state theory predictions for reaction rate values ignores the fact that the reaction may not proceed even with energy higher than the activation energy. For example, with initial conditions #4 discussed previously, the reactants approach each other with enough energy and reacts, but the product forms back the reactant species, so there is no reaction overall. This means that the transition state theory predicts reaction rate to be faster than the experimental rate.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is stronger (bond strength~ 565 kJ/mol<ref name=":0">Yoder, Claude. “Wired Chemist.” ''Common Bond Energies (D) and Bond Length (r)'', www.wiredchemist.com/chemistry/data/bond_energies_lengths.html.</ref>) than H-H bond (bond strength~ 432 kJ/mol<ref name=":0" />) because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals. H-F is highly polar while H-H bond is purely covalent. This means that the formation of H-F bond is favourable in the reaction F + H<sub>2</sub> even with the need to break the H-H bond and thus exothermic, while for the reverse reaction of H + HF, the breaking of H-F to make H-H bond is overall not stabilising and thus the reaction is endothermic. <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy).<br />
<br />
Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) The cases studied are an illustration of Polanyi's empirical rules. <br />
<br />
=== 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. ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = 0.1, p<sub>HH</sub> = -2.5<br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=789561MRD:ri3717 summer 20192019-05-23T11:14:16Z<p>Ri3717: /* Complete the table below 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. */</p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
ADDITIONAL----------------------------------------------------<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions #1<br />
</gallery><gallery>ri3717tableplot2.png|Initial conditions #2<br />
</gallery><gallery>ri3717tableplot3.png|Initial conditions #3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions #4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions #5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- the reactants and the transition state are in equilibrium<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
The transition state theory predictions for reaction rate values are ----'''EDIT'''--- than experimental values<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is stronger (bond strength~ 565 kJ/mol<ref name=":0">Yoder, Claude. “Wired Chemist.” ''Common Bond Energies (D) and Bond Length (r)'', www.wiredchemist.com/chemistry/data/bond_energies_lengths.html.</ref>) than H-H bond (bond strength~ 432 kJ/mol<ref name=":0" />) because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals. H-F is highly polar while H-H bond is purely covalent. This means that the formation of H-F bond is favourable in the reaction F + H<sub>2</sub> even with the need to break the H-H bond and thus exothermic, while for the reverse reaction of H + HF, the breaking of H-F to make H-H bond is overall not stabilising and thus the reaction is endothermic. <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy).<br />
<br />
Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) The cases studied are an illustration of Polanyi's empirical rules. <br />
<br />
=== 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. ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = 0.1, p<sub>HH</sub> = -2.5<br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=789445MRD:ri3717 summer 20192019-05-23T10:23:19Z<p>Ri3717: </p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
ADDITIONAL----------------------------------------------------<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions 1<br />
</gallery><gallery>ri3717tableplot2.png|Initial conditions 2<br />
</gallery><gallery>ri3717tableplot3.png|Initial conditions 3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions 4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions 5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is much stronger than H-H bond because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals, H-F is highly polar while H-H bond is purely covalent. In addition, H-F bond can form hydrogen bonds to other H-F molecules or molecules such as water, making <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
<br />
=== Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy). ===<br />
<br />
=== Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) ===<br />
The cases studied are an illustration of Polanyi's empirical rules. 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.<br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=789444MRD:ri3717 summer 20192019-05-23T10:22:54Z<p>Ri3717: </p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
File:Ri3717_plot1.png<br />
<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
ADDITIONAL----------------------------------------------------<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
<u>Dynamics</u><br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
<u>MEP</u><br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions 1<br />
</gallery><gallery><br />
ri3717tableplot2.png|Initial conditions 2<br />
</gallery><gallery><br />
ri3717tableplot3.png|Initial conditions 3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions 4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions 5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is much stronger than H-H bond because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals, H-F is highly polar while H-H bond is purely covalent. In addition, H-F bond can form hydrogen bonds to other H-F molecules or molecules such as water, making <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
<br />
=== Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy). ===<br />
<br />
=== Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) ===<br />
The cases studied are an illustration of Polanyi's empirical rules. 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.<br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=787652MRD:ri3717 summer 20192019-05-21T16:03:14Z<p>Ri3717: </p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery>where q<sub>1</sub> and q<sub>2</sub> are the reactant molecules, V is the potential energy.<br />
<br />
The transition state can be identified by starting trajectories near the transition state and if they move towards reactants or products (even with no initial momentum) then it is the transition state. It can be distinguished from a local minimum by calculating the second derivative, which gives a negative value for a local minimum but a positive value for a local maximum (i.e. the transition state).<br />
=== Report your best estimate of the transition state position ('''r<sub>ts</sub>''') for trajectories from r<sub>1</sub> = r<sub>2</sub> and explain your reasoning illustrating it with a “Internuclear Distances vs Time” plot for a relevant trajectory. ===<br />
The transition state position is the position at which the distance between A-B (r<sub>1</sub>) and B-C (r<sub>2</sub>) is equal, as it is symmetrical for this particular reaction. However, for trajectories from r<sub>1</sub> = r<sub>2</sub>, the H atoms perform oscillation, so the transition state position needs to be estimated by testing different r values. The transition state position (r<sub>ts</sub>) found with r<sub>1</sub> = r<sub>2</sub> is 0.908 Å. At this distance, there is almost no oscillation as shown in the Internuclear Distance vs Time plot below: <gallery><br />
Ri3717_plot1.png<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
ADDITIONAL----------------------------------------------------<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
Dynamics<br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
MEP<br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions 1<br />
</gallery><gallery><br />
ri3717tableplot2.png|Initial conditions 2<br />
</gallery><gallery><br />
ri3717tableplot3.png|Initial conditions 3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions 4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions 5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is much stronger than H-H bond because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals, H-F is highly polar while H-H bond is purely covalent. In addition, H-F bond can form hydrogen bonds to other H-F molecules or molecules such as water, making <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
<br />
=== Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy). ===<br />
<br />
=== Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) ===<br />
The cases studied are an illustration of Polanyi's empirical rules. 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.<br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:ri3717_summer_2019&diff=787624MRD:ri3717 summer 20192019-05-21T15:59:20Z<p>Ri3717: </p>
<hr />
<div>== Exercise 1: H+H<sub>2</sub> system ==<br />
<br />
=== 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? ===<br />
<br />
The transition state is mathematically defined as:<gallery><br />
File:ri3717_Eq.1<br />
</gallery><gallery><br />
Ri3717_plot1.png<br />
</gallery> <br />
<br />
This shows that at this value of r, the H atoms do not move with no initial momentum, which is characteristic of a transition state.<br />
<br />
ADDITIONAL----------------------------------------------------<br />
<br />
On the Internuclear Distance vs Time plot below, a H atom (A) and a H<sub>2</sub> molecule (B-C) approaching each other, resulting in a H<sub>2</sub> molecule (A-B) and a H atom (C).<gallery><br />
Ri3717_plot2.jpeg<br />
</gallery><br />
<br />
=== Comment on how the MEP and the trajectory you just calculated differ. ===<br />
<br />
For trajectories with r values below:<br />
<br />
r<sub>1</sub> = r<sub>ts</sub> + 0.01 = 0.909<br />
<br />
r<sub>2</sub> = r<sub>ts</sub> = 0.908,<br />
<br />
the MEP and Dynamics trajectories are compared.<gallery><br />
ri3717_ABC.png|Initial conditions of the three H atoms. Momenta= 0<br />
<br />
</gallery><br />
<br />
Dynamics<br />
<br />
Animation- B moves towards the C and A moves away from the rest. H atoms B and C continue to move to the right as they oscillate.<br />
<br />
Internuclear distances- stays constant for a short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases and fluctuates as the molecule performs an oscillation. At large t, the final value of B-C distance is approx. 0.75. <br />
<br />
Momenta- the momentum of A-B (p<sub>1</sub>(t)) increases with time; rapid increase at first then continues to slowly increase to a limit. The momentum of B-C (p<sub>2</sub>(t)) decreases first, then increases with fluctuation. At large t, p<sub>1</sub>(t) reaches a limit at 2.5 and p<sub>2</sub>(t) oscillates between 1.0-1.5, giving an average of 1.25.<br />
<br />
The angle θ stays constant at 0.<br />
<br />
MEP<br />
<br />
Animation- a smooth movement of the H atom in the centre towards the H atom on the right as the H atom on the left accelerates towards left.<br />
<br />
Internuclear distances- stays constant for a very short time and A-B and A-C distances increase as they move away from each other, while B-C distance decreases without fluctuation. At large t, the final value of B-C distance is approx. 0.75.<br />
<br />
Momenta- no change, constant at 0.<br />
<br />
When the r<sub>1</sub> and r<sub>2</sub> values are swapped, H atom A and C swap roles- A and B forms a molecule, C moves away to the right. <br />
<br />
=== Complete the table below 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. ===<br />
{| class="wikitable" border="1"<br />
!#<br />
! p<sub>1</sub> <sub>(kg.m/s)</sub> !! p<sub>2 (kg.m/s)</sub> !! E<sub>tot</sub> (kcal/mol) !! Reactive? !! Description of the dynamics<br />
|-<br />
|1<br />
| -1.25 || -2.5 ||-99.0||yes||As molecule A-B approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|2<br />
| -1.5 || -2.0 ||-100.5||no||Molecule A-B and atom C slowly approaches each other, and when they get to a certain distance, they repel and moves away from each other.<br />
|-<br />
|3<br />
| -1.5 || -2.5 ||-99.0||yes||As molecule A-B slowly approaches C, B is pulled away from A, forming molecule B-C. A moves away to the left, B-C moves to the right with oscillation.<br />
|-<br />
|4<br />
| -2.5 || -5.0 ||-85.0||no||Molecule A-B approaches C and B is pulled away from A. B-C oscillates but gets too close and repel each other, pushing B back to A, forming molecule A-B.<br />
|-<br />
|5<br />
| -2.5 || -5.2 ||-83.4||yes||Same as the one above happens, but molecule A-B oscillates again, gets too close and repel each other, pushing B back to C, finally forming molecule B-C.<br />
|}<br />
Although there is no simple trend in the reactivity and the initial conditions, It is evident that small changes to the initial conditions (momentum and hence the total energy) can affect the reactivity. For example based on the last two sets of initial conditions (conditions 4 and 5), we can see that increasing the magnitude of p<sub>2</sub> by 0.2 kg.m/s increases the total energy by 1.6 kcal/mol, and enables the reaction between molecule A-B and atom C, forming atom A and molecule B-C. <gallery><br />
ri3717tableplot1.png|Initial conditions 1<br />
</gallery><gallery><br />
ri3717tableplot2.png|Initial conditions 2<br />
</gallery><gallery><br />
ri3717tableplot3.png|Initial conditions 3<br />
</gallery><gallery><br />
ri3717tableplot4.png|Initial conditions 4<br />
</gallery><gallery><br />
ri3717tableplot5.png|Initial conditions 5<br />
</gallery><br />
<br />
=== 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? ===<br />
<br />
The main assumptions of Transition State Theory are<ref>Bligaard, T., and J.k. Nørskov. “Heterogeneous Catalysis.” ''Chemical Bonding at Surfaces and Interfaces'', 2008, pp. 255–321., doi:10.1016/b978-044452837-7.50005-8.</ref>:<br />
<br />
- the reactants are in thermal equilibrium and therefore the energy of the particles can be calculated by the Boltzmann equation<br />
<br />
- reactants that has reached the transition state with some velocity towards the product will not form back the reactants again.<br />
<br />
== Exercise 2-1: F-H-H system ==<br />
<br />
=== By inspecting the potential energy surfaces, classify the F + H<sub>2</sub> and H + HF reactions according to their energetics (endothermic or exothermic). How does this relate to the bond strength of the chemical species involved? ===<br />
F + H<sub>2</sub> is exothermic, H + HF is endothermic. <br />
<br />
H-F bond is much stronger than H-H bond because although both are covalent bonds and have good orbital overlap due to the same or very similar sized orbitals, H-F is highly polar while H-H bond is purely covalent. In addition, H-F bond can form hydrogen bonds to other H-F molecules or molecules such as water, making <br />
<br />
=== Locate the approximate position of the transition state. ===<br />
The transition state for the F-H-H system is not symmetrical, so the distance between F-H (r<sub>1</sub>) and H-H (r<sub>2</sub>) is not equal. With the initial conditions r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å, the three atoms F, H, H do not move as shown in the internuclear Distances vs Time plot below, which is indicative of a transition state. <gallery><br />
ri3717_plot34.png<br />
</gallery><br />
<br />
The surface plot also shows the position of the transition state at r<sub>1</sub>= 1.814 Å, and r<sub>2</sub> = 0.745 Å as the black spot on the graph is stationary. <gallery><br />
ri3717_plot35.png<br />
<br />
</gallery>Focusing on the reaction of F + H<sub>2</sub>, which is exothermic, the transition state is a "early" transition state. based on the Hammond's postulate, the structure of the transition state is energetically closer and similar in structure to the reactants. This agrees with the internuclear distances (r<sub>1 </sub>and r<sub>2</sub>) obtained for the transition state since the distance between the two H atoms is much shorter than the distance between F and H. <br />
<br />
=== Report the activation energy for both reactions. ===<br />
Now choosing a point close to the transition state, the set of initial conditions is r<sub>1</sub>= 1.804 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot36.png<br />
</gallery>The decrease in potential energy (hence the total energy) was determined from the graph as 29.9 kcal/mol. This is indicative of the energy difference between the transition state and the (F-H + H) state. Therefore this is the activation energy for the endothermic reaction between HF + H.<br />
<br />
For the activation energy of the reaction F + H<sub>2</sub>, another set of initial conditions is tested: r<sub>1</sub>= 1.824 Å, and r<sub>2</sub> = 0.745 Å. This yielded the following Energy vs Time graph:<gallery><br />
ri3717plot7.png<br />
</gallery>The energy change is very small even at a very large value of t (t= 3000). The activation energy of the reaction F + H<sub>2</sub> is estimated to be 0.2 kcal/mol.<br />
<br />
=== Identify a set of initial conditions that results in a reactive trajectory for the F + H<sub>2</sub>, and look at the “Animation” and “Momenta vs Time”. 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. ===<br />
Initial conditions: r<sub>1</sub>= 2.0, r<sub>2</sub> = 0.7, p<sub>1</sub>= -0.7, p<sub>2</sub> = 0 <br />
<br />
Observations from Animation: The H<sub>2</sub> molecule moves towards F and one of the H atoms gets pulled towards F. Then it is bounced back to H, vibrates, and forms back H-F and H in the end. <br />
<br />
As shown in the Momenta vs Time graph below, the overall momentum has increased after reaction. The reaction energy has been transferred to the products in the form of kinetic energy (vibration). <gallery><br />
ri3717plotmomentum.png|Momenta vs Time<br />
</gallery>This could be confirmed experimentally by monitoring the change in temperature as the energy could be released to or absorbed from the environment as heat. As F+H<sub>2</sub> is an exothermic reaction, the temperature is expected to increase on reaction. <br />
<br />
=== Setup a calculation starting on the side of the reactants of F + H<sub>2</sub>, at the bottom of the well r<sub>HH</sub> = 0.74, with a momentum p<sub>FH</sub> = -0.5, and explore several values of p<sub>HH</sub> in the range -3 to 3 (explore values also close to these limits). What do you observe? Note that we are putting a significant amount of energy (much more than the activation energy) into the system on the H - H vibration. ===<br />
For initial conditions r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.5, different values of p<sub>HH</sub> between -3 and 3 were tested and results are shown below.<br />
{| class="wikitable"<br />
!#<br />
!p<sub>HH</sub> (kg.m/s)<br />
!Reaction?<br />
!Observation<br />
|-<br />
|1<br />
|<nowiki>-3.0</nowiki><br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H. <br />
|-<br />
|2<br />
|<nowiki>-2.9</nowiki><br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|3<br />
|<nowiki>-2.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|4<br />
|<nowiki>-1.0</nowiki><br />
|yes<br />
|same as above but reaction happens more slowly.<br />
|-<br />
|5<br />
|0<br />
|no<br />
|H<sub>2</sub> molecule vibrates and moves towards the F atom until it gets repelled by F and moves away.<br />
|-<br />
|6<br />
|1.0<br />
|yes<br />
|H<sub>2</sub> molecule moves closer to the F atom as it vibrates, and eventually one of the H atoms forms a bond with F. The remaining H gets repelled and moves away, resulting in H-F and H. <br />
|-<br />
|7<br />
|2.0<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|8<br />
|2.9<br />
|yes<br />
|Same as above but reaction happens more quickly.<br />
|-<br />
|9<br />
|3.0<br />
|no<br />
|H-H molecule vibrates for a while, then one of the H atoms gets closer to F, forming H-F for a very short while. Then the H atom gets pushed back and forms back H-H.<br />
|}<br />
<br />
=== For the same initial position, increase slightly the momentum p<sub>FH</sub> = -0.8, and considerably reduce the overall energy of the system by reducing the momentum p<sub>HH</sub> = 0.1. What do you observe now? ===<br />
Initial conditions: r<sub>FH</sub> = 2.10, r<sub>HH</sub> = 0.74 and p<sub>FH</sub> = -0.8, p<sub>HH</sub> = 0.1<gallery><br />
ri3717Hahb.png|Starting positions of F and H-H<br />
</gallery>Observation: A vibrating hydrogen molecule slowly approaches an F atom. One of the H atoms (H<sub>A</sub>) gets pulled towards the F atom, producing F-H<sub>A</sub> and H<sub>B</sub>, but H<sub>A</sub> gets repelled and moves back towards H<sub>B</sub>, producing back the reactant, F and H-H. Then the H<sub>A</sub> atom gets repelled by H<sub>B</sub> and bonds to F again, ending with F-H and H.<gallery><br />
ri3717plot0.png|Contour plot of the reaction<br />
</gallery><br />
<br />
== Exercise 2-2: H + HF System ==<br />
<br />
=== Setup initial conditions starting at the bottom of the entry channel, with very low vibrational motion on on the H - F bond, and an arbitrarily high value of p<sub>HH</sub> above the activation energy (an H atom colliding with a high kinetic energy). ===<br />
<br />
=== Try to obtain a reactive trajectory by decreasing the momentum of the incoming H atom and increasing the energy of the H - F vibration. (It may be difficult to find the initial conditions that generate a reactive trajectory for this reaction. Using the inversion of momentum procedure for a trajectory starting on the transition state can be useful in this case. Working on the Skew Plot framework could also be helpful.) ===<br />
The cases studied are an illustration of Polanyi's empirical rules. 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.<br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776529Rep:Mod:Inorganic ri3717 summer 20192019-05-10T16:34:21Z<p>Ri3717: /* Mini project: Ionic liquids */</p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Total energy using 3-21G optimisation = -26.46226371 a.u.<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Total energy using 6-31G optimisation = -26.61532360 a.u.<br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404<br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
</gallery><br />
<br />
Bonding orbital<br />
<br />
<gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><br />
<br />
partially antibonding -- C-N interactions are antibonding through space.<br />
<br />
<gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16</gallery><br />
<br />
partially antibonding -- C-N interactions are antibonding through space.<br />
<br />
<gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776474Rep:Mod:Inorganic ri3717 summer 20192019-05-10T16:27:29Z<p>Ri3717: /* NI3 optimisation (GEN) */</p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Total energy using 3-21G optimisation = -26.46226371 a.u.<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Total energy using 6-31G optimisation = -26.61532360 a.u.<br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404<br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776457Rep:Mod:Inorganic ri3717 summer 20192019-05-10T16:24:28Z<p>Ri3717: /* BH3 optimisation (6-31G) */</p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Total energy using 3-21G optimisation = -26.46226371 a.u.<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Total energy using 6-31G optimisation = -26.61532360 a.u.<br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776452Rep:Mod:Inorganic ri3717 summer 20192019-05-10T16:23:18Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Total energy using 3-21G optimisation = -26.46226371 a.u.<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776441Rep:Mod:Inorganic ri3717 summer 20192019-05-10T16:21:22Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776296Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:59:50Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776293Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:59:31Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
Association energy, ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
Bond energy of B-H= <br />
Bond energy of N-H=<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776192Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:47:04Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised NI3 Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH3)4]+ Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776164Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:44:42Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717_NI3_FREQ.LOG|thumb|RI3717_NI3_FREQ.LOG|none]]<br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776150Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:42:57Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised BH3 molecule</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717 BH3 FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NI3_FREQ.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
<jmol><jmolApplet><br />
<title>Optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> Ion</title><br />
<color>black</color><br />
<size>200</size><br />
<uploadedFileContents>RI3717_NCH34+_SYM_OPT.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:RI3717_NI3_FREQ.LOG&diff=776146File:RI3717 NI3 FREQ.LOG2019-05-10T15:42:28Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776130Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:39:52Z<p>Ri3717: /* BH3 optimisation (3-21G) */</p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|A2<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|E<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|A1<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|E<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised NI<sub>3</sub><br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776070Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:33:10Z<p>Ri3717: /* Mini project: Ionic liquids */</p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <gallery><br />
File:Ri3717Charge distribution, n.PNG|Charge distribution for [N(CH3)4]+<br />
<br />
</gallery><gallery><br />
File:Ri3717Charge distribution, p.PNG|Charge distribution for [P(CH3)4]+<br />
<br />
</gallery> <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:Ri3717MO20.PNG|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
File:Ri3717MO17.PNG|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717Charge_distribution,_p.PNG&diff=776065File:Ri3717Charge distribution, p.PNG2019-05-10T15:31:58Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717Charge_distribution,_n.PNG&diff=776056File:Ri3717Charge distribution, n.PNG2019-05-10T15:31:03Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776035Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:28:26Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
File:ri3717MO20.png|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
ri3717MO17.png|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
File:Ri3717MO16.PNG|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=776020Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:26:37Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
ri3717MO20.png|Molecular orbital #20<br />
<br />
</gallery><gallery><br />
ri3717im20.jpg|Formation of molecular orbital #20<br />
</gallery><br />
<br />
MO#17<gallery><br />
ri3717MO17.png|Molecular orbital #17<br />
</gallery><gallery><br />
ri3717im17.jpg|Formation of molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
ri3717MO16.png|Molecular orbital #16<br />
<br />
</gallery><gallery><br />
ri3717im16.jpg|Formation of molecular orbital #16<br />
</gallery><br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717im20.jpg&diff=776014File:Ri3717im20.jpg2019-05-10T15:26:14Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717im17.jpg&diff=776010File:Ri3717im17.jpg2019-05-10T15:25:36Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717im16.jpg&diff=775995File:Ri3717im16.jpg2019-05-10T15:23:54Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=775972Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:20:55Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied'''<br />
<br />
MO#20<gallery><br />
ri3717MO20.png|Molecular orbital #20<br />
<br />
</gallery><br />
<br />
MO#17<gallery><br />
ri3717MO17.png|Molecular orbital #17<br />
</gallery><br />
<br />
MO#16<gallery><br />
ri3717MO16.png|Molecular orbital #16<br />
<br />
</gallery> <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717MO16.PNG&diff=775958File:Ri3717MO16.PNG2019-05-10T15:19:13Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717MO17.PNG&diff=775957File:Ri3717MO17.PNG2019-05-10T15:19:00Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717MO20.PNG&diff=775954File:Ri3717MO20.PNG2019-05-10T15:18:27Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=775854Rep:Mod:Inorganic ri3717 summer 20192019-05-10T15:05:02Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. These are both reflected in the charge distribution of these ions in the table above. <br />
<br />
[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: The charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is about half negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because the carbon atoms in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> is bonded to a strongly electronegative atom, N. The central N atom draws electron density towards itself, resulting in a slight negative charge of -0.295 even though the whole ion is positively charged. The positive charge is on the H atoms in the methl groups. <br />
<br />
[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>: In the bonding between C and P, more electron density is pulled towards the C atom as it is more electronegative than P. The central P atom experiences the pull of electron density from the four methyl groups, resulting in a +1.667 charge. H atoms also hold some positive charges. <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=775665Rep:Mod:Inorganic ri3717 summer 20192019-05-10T14:43:06Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. <br />
<br />
The charge distribution in C-N bond for [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. This is because <br />
<br />
What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom, although in reality the charge is spread out on the whole ion. From the charge distribution obtained for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> above, we can see that the positive charge is in deed not on the N atom but on hydrogen atoms. <br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=775020Rep:Mod:Inorganic ri3717 summer 20192019-05-10T13:31:11Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000132 0.000450 YES<br />
RMS Force 0.000062 0.000300 YES<br />
Maximum Displacement 0.001114 0.001800 YES<br />
RMS Displacement 0.000491 0.001200 YES<br />
Predicted change in Energy=-6.321232D-07<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000035 0.000450 YES<br />
RMS Force 0.000010 0.000300 YES<br />
Maximum Displacement 0.000241 0.001800 YES<br />
RMS Displacement 0.000133 0.001200 YES<br />
Predicted change in Energy=-2.345703D-08<br />
Optimization completed.</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. However, the charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. N is positively charged----- <br />
<br />
<nowiki> </nowiki>What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom<br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774990Rep:Mod:Inorganic ri3717 summer 20192019-05-10T13:26:33Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000011 0.000300 YES<br />
Maximum Displacement 0.000117 0.001800 YES<br />
RMS Displacement 0.000087 0.001200 YES<br />
Predicted change in Energy=-1.935227D-08<br />
Optimization completed.<br />
</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.060</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|}<br />
<br />
<nowiki> </nowiki>Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. However, the charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. N is positively charged----- <br />
<br />
<nowiki> </nowiki>What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom<br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774931Rep:Mod:Inorganic ri3717 summer 20192019-05-10T13:17:16Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
{| class="wikitable"<br />
!Mode #<br />
!Wavenumber (cm<sup>-1</sup>)<br />
!Intensity (arbitrary units)<br />
!Symmetry<br />
!IR active?<br />
!Description<br />
|-<br />
|1<br />
|1163<br />
|93<br />
|<br />
|yes<br />
|out-of-plane bend<br />
|-<br />
|2<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|bend<br />
|-<br />
|3<br />
|1213<br />
|14<br />
|<br />
|yes<br />
|asymmetric bend<br />
|-<br />
|4<br />
|2582<br />
|0<br />
|<br />
|no<br />
|symmetric stretch<br />
|-<br />
|5<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|-<br />
|6<br />
|2716<br />
|126<br />
|<br />
|yes<br />
|asymmetric stretch<br />
|}<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
Qualitative MO theory is useful to a large extent when making predictions and understanding the interactions between how atomic orbitals interact to form molecular orbitals. However, there is still a need for us to understand that MO theory may not fully represent the actual orbital interactions.<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<strong>File:Ri3717 GEN NI3 OPTIMISATION.LOG</strong> <br />
<br />
Optimised N-I distance= 2.18404 <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000011 0.000300 YES<br />
Maximum Displacement 0.000117 0.001800 YES<br />
RMS Displacement 0.000087 0.001200 YES<br />
Predicted change in Energy=-1.935227D-08<br />
Optimization completed.<br />
</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.050</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|}<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. However, the charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. N is positively charged----- <br />
<br />
<nowiki> </nowiki>What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom<br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774754Rep:Mod:Inorganic ri3717 summer 20192019-05-10T12:44:26Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
ADD TABLE OF VIBRATIONS<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<br />
what is your optimised N-I distance? <br />
<br />
Optimised N-I distance= <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000011 0.000300 YES<br />
Maximum Displacement 0.000117 0.001800 YES<br />
RMS Displacement 0.000087 0.001200 YES<br />
Predicted change in Energy=-1.935227D-08<br />
Optimization completed.<br />
</pre><br />
<br />
Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<pre><br />
Low frequencies --- -0.0031 -0.0008 0.0007 50.6301 50.6301 50.6302<br />
Low frequencies --- 187.9221 213.0069 213.0069</pre><br />
<br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.050</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|}<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. However, the charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. N is positively charged----- <br />
<br />
<nowiki> </nowiki>What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom<br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774748Rep:Mod:Inorganic ri3717 summer 20192019-05-10T12:42:08Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
ADD TABLE OF VIBRATIONS<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<br />
what is your optimised N-I distance? <br />
<br />
Optimised N-I distance= <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<gallery><br />
File:ri3717_NCH34+_6-31G_summary.PNG|Summary table for optimised [N(CH3)4]+ ion<br />
</gallery><br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
<gallery><br />
File:ri3717_PCH34+_6-31G_summary.PNG|Summary table for optimised [P(CH3)4]+ ion<br />
</gallery>Item table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<nowiki> </nowiki>Low frequencies table for optimised [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<br />
<nowiki> </nowiki>Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.050</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|}<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. However, the charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. N is positively charged----- <br />
<br />
<nowiki> </nowiki>What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom<br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717_PCH34%2B_6-31G_summary.PNG&diff=774721File:Ri3717 PCH34+ 6-31G summary.PNG2019-05-10T12:39:47Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717_NCH34%2B_6-31G_summary.PNG&diff=774714File:Ri3717 NCH34+ 6-31G summary.PNG2019-05-10T12:38:33Z<p>Ri3717: </p>
<hr />
<div></div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774348Rep:Mod:Inorganic ri3717 summer 20192019-05-10T09:35:20Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
<br />
RI3717 BH3 FREQ.LOG<br />
<br />
ADD TABLE OF VIBRATIONS<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<br />
what is your optimised N-I distance? <br />
<br />
Optimised N-I distance= <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.050</nowiki><br />
|<nowiki>+0.298</nowiki><br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|<nowiki>+0.269</nowiki><br />
|}<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Considering the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, C-N bond is expected to be polar with more electron density towards N, and C-P bond is polar with more electron density towards C. C-P bond polarity is reflected in the charge distribution in the ion [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>, where C is more negatively charged than P as shown in the table above. However, the charge distribution in C-N bond for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> shows that C is more than twice as negatively charged than the C in [P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>. N is positively charged----- <br />
<br />
<nowiki> </nowiki>What does the "formal" positive charge on the N represent in the traditional picture?<br />
<br />
It represents a +1 charge on the N atom<br />
<br />
On what atoms is the positive charge actually located for this cation?<br />
<br />
There could be a slight positive charge on the substituents such as H (+0.298 for [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>), but a significant amount of positive charge is located on N (+1.667 in the case of [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup>). <br />
<br />
'''Three valence MOs, occupied''' <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774332Rep:Mod:Inorganic ri3717 summer 20192019-05-10T09:13:23Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
RI3717 BH3 FREQ.LOG<br />
<br />
ADD TABLE OF VIBRATIONS<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
MO diagram of BH3. Original image <ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Important differences between the real and LCAO MOs are that real MOs are more diffuse and have an overall shape of the overlapping atomic orbitals. <br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to my completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file <br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<br />
what is your optimised N-I distance? <br />
<br />
Optimised N-I distance= <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.050</nowiki><br />
|0.298<br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|0.269<br />
|}<br />
Electronegativity of N is 3.04<ref>Winter, Mark. “Nitrogen: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/nitrogen/electronegativity.html.</ref>, that of P is 2.19<ref>Winter, Mark. “Phosphorus: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/phosphorus/electronegativity.html.</ref>. Compared with the electronegativity of C, which is 2.55<ref>Winter, Mark. “Carbon: Electronegativity.” ''WebElements Periodic Table'', WebElements Ltd, www.webelements.com/carbon/electronegativity.html.</ref>, <br />
<br />
== References ==</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:Inorganic_ri3717_summer_2019&diff=774030Rep:Mod:Inorganic ri3717 summer 20192019-05-09T21:50:08Z<p>Ri3717: </p>
<hr />
<div>== EX3 ==<br />
<br />
=== BH<sub>3</sub> optimisation (3-21G) ===<br />
<gallery><br />
ri3717_BH3_optimised.png|Optimised BH3 molecule<br />
</gallery><gallery><br />
ri3717BH3_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000217 0.000450 YES<br />
RMS Force 0.000105 0.000300 YES<br />
Maximum Displacement 0.000900 0.001800 YES<br />
RMS Displacement 0.000441 0.001200 YES<br />
Predicted change in Energy=-1.635269D-07<br />
Optimization completed.</pre><br />
<br />
Item table for optimised BH<sub>3</sub> moleucule<br />
<br />
Total energy (Hartree) using 3-21G optimisation = -26.4623<br />
=== <br> BH<sub>3</sub> optimisation (6-31G) ===<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000012 0.000450 YES<br />
RMS Force 0.000008 0.000300 YES<br />
Maximum Displacement 0.000064 0.001800 YES<br />
RMS Displacement 0.000039 0.001200 YES<br />
Predicted change in Energy=-1.131126D-09<br />
Optimization completed.</pre><br />
<br />
Total energy (Hartree) using 6-31G optimisation = -26.6153<gallery><br />
ri3717BH3_6-31g_summary.PNG|Summary table for optimised BH3 molecule<br />
</gallery><br />
<br />
Low frequencies table for for optimised BH<sub>3</sub><br />
<pre><br />
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165<br />
Low frequencies --- 1162.9519 1213.1527 1213.1554</pre><br />
<br />
[[File:RI3717 BH3 FREQ.LOG|thumb|ri3717_BH3_freq.log|none]]<br />
<br />
JMOL<br />
RI3717 BH3 FREQ.LOG<br />
<br />
ADD TABLE OF VIBRATIONS<br />
<br />
<gallery><br />
BH3_IR_spectrum.PNG|IR spectrum for BH3 <br />
</gallery><br />
<br />
In the IR spectrum for BH3, there appears to be three peaks (1163, 1213, 2716 cm]<sup>-1</sup>) although there are six vibrations. This is because some of the vibrations have very close or equal vibration frequencies, or zero intensity because the vibration is symmetrical and not IR active. Peaks from modes 2 and 3 overlap, so do 5 and 6, and mode 4 has zero intensity, resulting in three peaks in total.<br />
<br />
<br />
<br />
MO diagram of BH3<ref>Hunt, Patricia. “Lecture 4 Tutorial Problem Model Answers.” 9 May 2019.</ref><gallery><br />
File:ri3717Doc1.jpg|MO diagram for BH3<br />
</gallery><br />
<br />
<br />
Are there any significant differences between the real and LCAO MOs?<br />
<br />
What does this say about the accuracy and usefulness of qualitative MO theory?<br />
<br />
<br />
=== NH<sub>3</sub> optimisation (6-31G) ===<br />
E(NH3)= -56.55776872 a.u.<br />
<br />
E(BH3)= -26.61532360 a.u.<br />
<br />
E(NH3BH3)= -83.22468893 a.u.<br />
<br />
<br />
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]<br />
= -83.22468893 -[-56.55776872 -26.61532360]<br />
= -0.05159661 a.u.<br />
<br />
Based on the energy calculation above, the B-N dative bond is weak compared to other bonds such as C-C (~350 kJ/mol) or C-N (~300 kJ/mol).<br />
<br />
1 a.u.= 2625.5 kJ/mol<br />
-0.05159661 a.u.= -135.466873 kJ/mol<br />
<br />
<br />
=== NI<sub>3</sub> optimisation (GEN) ===<br />
<br />
Link to your completed B3LYP/6-31G(d,p)LANL2DZ NI3 frequency file on your wiki<br />
<br />
[[File:ri3717_GEN_NI3_OPTIMISATION.LOG|thumb|ri3717_GEN_NI3_optimisation.log|none]]<br />
<br />
<br />
<gallery><br />
ri3717_NI3_optimisation_summary_table.PNG|Summary table for optimised NI3 molecule<br />
</gallery><br />
<br />
<br />
Item table for optimised NI<sub>3</sub><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000061 0.000450 YES<br />
RMS Force 0.000037 0.000300 YES<br />
Maximum Displacement 0.000459 0.001800 YES<br />
RMS Displacement 0.000285 0.001200 YES<br />
Predicted change in Energy=-3.108653D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Include the low frequencies lines in your wiki<br />
<br />
<br />
Include a Jmol image of your optimised geometry in your wiki<br />
<br />
<br />
what is your optimised N-I distance?<br />
Optimised N-I distance= <br />
<br />
==Mini project: Ionic liquids==<br />
=== [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> optimisation (6-31G d,p) ===<br />
<br />
JMOL<br />
RI3717_NCH34+_SYM_OPT.LOG<br />
<br />
[[File:RI3717 NCH34+ SYM OPT.LOG|none|thumb|RI3717_NCH34+_SYM_OPT.log]]<br />
<br />
Item table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000062 0.000450 YES<br />
RMS Force 0.000025 0.000300 YES<br />
Maximum Displacement 0.000143 0.001800 YES<br />
RMS Displacement 0.000060 0.001200 YES<br />
Predicted change in Energy=-7.919745D-08<br />
Optimization completed.</pre><br />
<br />
<br />
Low frequencies table for optimised [N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup> <br />
<pre><br />
Low frequencies --- 0.0007 0.0011 0.0012 35.1707 35.1707 35.1707<br />
Low frequencies --- 218.6022 317.3460 317.3460</pre><br />
<br />
Comparing charge distribution <br />
{| class="wikitable"<br />
!Charge distribution<br />
!Central atom (N or P)<br />
!C<br />
!H<br />
|-<br />
|[N(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>+1.667</nowiki><br />
|<nowiki>-1.050</nowiki><br />
|0.298<br />
|-<br />
|[P(CH<sub>3</sub>)<sub>4</sub>]<sup>+</sup><br />
|<nowiki>-0.295</nowiki><br />
|<nowiki>-0.483</nowiki><br />
|0.269<br />
|}</div>Ri3717https://chemwiki.ch.ic.ac.uk/index.php?title=File:Ri3717Doc1.jpg&diff=774022File:Ri3717Doc1.jpg2019-05-09T21:42:16Z<p>Ri3717: </p>
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