https://chemwiki.ch.ic.ac.uk/api.php?action=feedcontributions&feedformat=atom&user=Zm1116ChemWiki - User contributions [en]2026-04-07T21:13:15ZUser contributionsMediaWiki 1.43.0https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=713917MRD:011967752018-05-11T16:09:32Z<p>Zm1116: /* Reactive and unreactive trajectories */</p>
<hr />
<div>[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
== EXERCISE 1: H + H<sub>2</sub> system ==<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero in one direction (a maximum), and larger than zero in the perpendicular direction (a minimum), implying that it is a saddle point.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1), in which it can be seen that the nuclei do not vibrate as they have no kinetic energy, i.e. they are not moving along any energy gradients and the system is balanced at the transition state.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum, or in other words the bond has vibrational energy.<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough momentum (kinetic energy) to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|Reaction crosses over transition state and then returns to reactants, with vigorous bond vibration at completion<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|Reaction proceeds vigorously with movement over higher energy forms of the transition state and initially reversion, on the way to the products<br />
|}<br />
'''Assumptions in transition state theory'''<br />
# The Born-Oppenheimer approximation is used, meaning that quantum tunnelling by electrons is not considered<ref name=":0"><nowiki>https://www.sciencedirect.com/topics/chemistry/transition-state-theory (accessed 08/05/2018)</nowiki></ref>. This means that motion along the reaction coordinate can be considered as a classical translation<ref name=":1">J. I. Steinfeld, J. S. Francisco, W. L. Hase, Chemical Kinetic and Dynamics, Prentice-Hall, United States, 1989</ref>.<br />
# The energies of the transition states which are reacting to form products follow the Boltzmann distribution, even when the reaction has not yet reached dynamic equilibrium<ref name=":1" />.<br />
# Once the transition state has been reached and there is momentum in the direction of the products, there will be no reversion to reactants<ref name=":0" />.<br />
These assumptions are however observed to be incorrect according to these simulations, as the fourth simulation shows the reactants crossing the transition state and then returning. Transition state theory would agree well with the experimental rate values for reactions which follow its assumptions, such as the first, second and third reactions, but would give poor approximations to the final two. In the fourth simulation, the third assumption of transition state theory is broken; the reaction crosses the transition state and then reverts to the reactants. This shows that it is a simplification to claim that it is only momentum in the direction of the products is required, and there are cases where too much energy is supplied and the product bond vibrates so violently that it shakes itself apart to products again. The fifth case demonstrates that this barrier recrossing can happen multiple times, if more vibrational energy is supplied. Transition state theory would predict a higher rate than experimental values in the fourth and fifth cases as it does not account for the time spent on reversion.<br />
<br />
== EXERCISE 2: F - H - H system ==<br />
[[File:Transition state zohar.PNG|thumb|Fig. 3: Surface plot for the F + H<sub>2</sub> reaction, with the reactants (F + H<sub>2</sub>) on the higher energy, right hand side and the products (H + HF) on the lower energy, left hand side.]]<br />
The F + H<sub>2</sub> reaction is exothermic and the H + HF reaction is endothermic as the F + H<sub>2</sub> system lies on the higher energy side of the surface plot (Fig. 3) and H + HF on the lower energy side. This implies that the H-F bond is stronger than the H-H bond. The transition state is located at AB distance 1.808 and BC distance 0.751. This was identified as it was within the BC = 0.751 energy trough, and far enough along the AB separation that the system remained balanced at the transition state and did not slide to the products.<br />
The potential energy of the transition state is -103.738 kcal/mol, that of F + H<sub>2</sub> is -103.793 kcal/mol and that of H + HF is -133.772 kcal/mol. Therefore the activation energy for the formation of H + HF is +0.055 kcal/mol and the activation energy for the formation of F + H<sub>2</sub> is +30.034 kJ/mol.<br />
The reaction energy is released by the greater amplitude of vibration of the H-F product bond compared to the H-H reactant bond, therefore dissipating the energy to the surroundings through kinetic motion (Fig. 4), though the simulation doesn't show this eventual removal of energy from the system. This could be confirmed experimentally by measuring an increase in temperature during the reaction as energy is transferred to the surroundings by this increased amplitude of bond vibration.<br />
[[File:Momenta zohar.PNG|thumb|Fig. 4: Internuclear momenta for the reaction of F + H<sub>2</sub>, showing that the H + HF products have greater internuclear momenta than the reactants.]]'''Polanyi's empirical rules'''[[File:Trajectory zohar.PNG|thumb|Fig. 5: Reactive trajectory from H + HF to F + H2]]<br />
A reactive trajectory is obtained with an AB distance of 0.92, BC distance of 2.23, AB momentum of -10 and BC momentum of -1 (Fig. 5). This relates to Polanyi's empirical rules, which state that kinetic/translational energy is ineffective in causing a system to cross a late transition state (i.e. that of the endothermic reaction of HF + H) and that only vibrational energy is effective in crossing such a barrier<ref><nowiki>http://brouard.chem.ox.ac.uk/teaching/dynlectures4to6.pdf (Accessed 10/05/2018)</nowiki></ref>. This leads to the release of energy by product translation rather than by product bond vibration, after the reaction has proceeded. The vibrational energy supplied is represented in the simulation as momentum between F and H, and it is observable in Fig. 5 that the product H-H bond has less momentum, or lower amplitude vibration than the reactant H-F bond at the start of the reaction, and that the H<sub>2</sub> product translates away from F. The inverse of all the above statements is true for an early transition state, as in the case of the reaction of F + H<sub>2</sub>, and it is thus observed that only translational energy is able to cause crossing of the transition state and that the products release their energy by bond vibration, shown in Fig. 4 as greater internuclear momentum in the product H-F bond.<br />
<br />
'''References'''</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=713541MRD:011967752018-05-11T15:32:21Z<p>Zm1116: /* EXERCISE 2: F - H - H system */</p>
<hr />
<div>[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
== EXERCISE 1: H + H<sub>2</sub> system ==<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|Reaction crosses over transition state and then returns to reactants, with vigorous bond vibration<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|Reaction proceeds vigorously with movement over higher energy forms of the transition state and initially reversion, on the way to the products<br />
|}<br />
'''Assumptions in transition state theory'''<br />
# The Born-Oppenheimer approximation is used, meaning that quantum tunnelling by electrons is not considered<ref name=":0"><nowiki>https://www.sciencedirect.com/topics/chemistry/transition-state-theory (accessed 08/05/2018)</nowiki></ref>. This means that motion along the reaction coordinate can be considered as a classical translation<ref name=":1">J. I. Steinfeld, J. S. Francisco, W. L. Hase, Chemical Kinetic and Dynamics, Prentice-Hall, United States, 1989</ref>.<br />
# The energies of the transition states which are reacting to form products follow the Boltzmann distribution, even when the reaction has not yet reached dynamic equilibrium<ref name=":1" />.<br />
# Once the transition state has been reached and there is momentum in the direction of the products, there will be no reversion to reactants<ref name=":0" />.<br />
These assumptions are however observed to be incorrect according to these simulations, as the fourth simulation shows the reactants crossing the transition state and then returning. Transition state theory would agree well with the experimental rate values for reactions which follow its assumptions, such as the first, second and third reactions, but would give poor approximations to the final two. In the fourth simulation, the third assumption of transition state theory is broken; the reaction crosses the transition state and then reverts to the reactants. This shows that it is a simplification to claim that it is only momentum in the direction of the products is required, and there are cases where too much energy is supplied and the product bond vibrates so violently that it shakes itself apart to products again. The fifth case demonstrates that this barrier recrossing can happen multiple times, if more vibrational energy is supplied.<br />
<br />
== EXERCISE 2: F - H - H system ==<br />
[[File:Transition state zohar.PNG|thumb|Fig. 3: Surface plot for the F + H<sub>2</sub> reaction, with the reactants (F + H<sub>2</sub>) on the higher energy, right hand side and the products (H + HF) on the lower energy, left hand side.]]<br />
The F + H<sub>2</sub> reaction is exothermic and the H + HF reaction is endothermic as the F + H<sub>2</sub> system lies on the higher energy side of the surface plot (Fig. 3) and H + HF on the lower energy side. This implies that the H-F bond is stronger than the H-H bond. The transition state is located at AB distance 1.808 and BC distance 0.751. This was identified as it was within the BC = 0.751 energy trough, and far enough along the AB separation that the system remained balanced at the transition state and did not slide to the products.<br />
The potential energy of the transition state is -103.738 kcal/mol, that of F + H<sub>2</sub> is -103.793 kcal/mol and that of H + HF is -133.772 kcal/mol. Therefore the activation energy for the formation of H + HF is +0.055 kcal/mol and the activation energy for the formation of F + H<sub>2</sub> is +30.034 kJ/mol.<br />
The reaction energy is released by the greater amplitude of vibration of the H-F product bond compared to the H-H reactant bond, therefore dissipating the energy to the surroundings through kinetic motion (Fig. 4), though the simulation doesn't show this eventual removal of energy from the system. This could be confirmed experimentally by measuring an increase in temperature during the reaction as energy is transferred to the surroundings by this increased amplitude of bond vibration.<br />
[[File:Momenta zohar.PNG|thumb|Fig. 4: Internuclear momenta for the reaction of F + H<sub>2</sub>, showing that the H + HF products have greater internuclear momenta than the reactants.]]<br />
[[File:Trajectory zohar.PNG|thumb|Fig. 5: Reactive trajectory from H + HF to F + H2]]<br />
A reactive trajectory is obtained with an AB distance of 0.92, BC distance of 2.23, AB momentum of -10 and BC momentum of -1 (Fig. 5). This relates to Polanyi's empirical rules, which state that kinetic/translational energy is ineffective in causing a system to cross a late transition state (i.e. that of the endothermic reaction of HF + H) and that only vibrational energy is effective in crossing such a barrier<ref><nowiki>http://brouard.chem.ox.ac.uk/teaching/dynlectures4to6.pdf (Accessed 10/05/2018)</nowiki></ref>. This leads to the release of energy by product translation rather than by product bond vibration, after the reaction has proceeded. The vibrational energy supplied is represented in the simulation as momentum between F and H, i.e. high amplitude vibration of the H-F reactant bond until it dissociates and the hydrogens collide and translate away from F.<br />
<br />
'''References'''</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=713279MRD:011967752018-05-11T15:06:42Z<p>Zm1116: </p>
<hr />
<div>[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
== EXERCISE 1: H + H<sub>2</sub> system ==<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|Reaction crosses over transition state and then returns to reactants, with vigorous bond vibration<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|Reaction proceeds vigorously with movement over higher energy forms of the transition state and initially reversion, on the way to the products<br />
|}<br />
'''Assumptions in transition state theory'''<br />
# The Born-Oppenheimer approximation is used, meaning that quantum tunnelling by electrons is not considered<ref name=":0"><nowiki>https://www.sciencedirect.com/topics/chemistry/transition-state-theory (accessed 08/05/2018)</nowiki></ref>. This means that motion along the reaction coordinate can be considered as a classical translation<ref name=":1">J. I. Steinfeld, J. S. Francisco, W. L. Hase, Chemical Kinetic and Dynamics, Prentice-Hall, United States, 1989</ref>.<br />
# The energies of the transition states which are reacting to form products follow the Boltzmann distribution, even when the reaction has not yet reached dynamic equilibrium<ref name=":1" />.<br />
# Once the transition state has been reached and there is momentum in the direction of the products, there will be no reversion to reactants<ref name=":0" />.<br />
These assumptions are however observed to be incorrect according to these simulations, as the fourth simulation shows the reactants crossing the transition state and then returning. Transition state theory would agree well with the experimental rate values for reactions which follow its assumptions, such as the first, second and third reactions, but would give poor approximations to the final two. In the fourth simulation, the third assumption of transition state theory is broken; the reaction crosses the transition state and then reverts to the reactants. This shows that it is a simplification to claim that it is only momentum in the direction of the products is required, and there are cases where too much energy is supplied and the product bond vibrates so violently that it shakes itself apart to products again. The fifth case demonstrates that this barrier recrossing can happen multiple times, if more vibrational energy is supplied.<br />
<br />
== EXERCISE 2: F - H - H system ==<br />
[[File:Transition state zohar.PNG|thumb|Fig. 3: Surface plot for the F + H<sub>2</sub> reaction, with the reactants (F + H<sub>2</sub>) on the higher energy, right hand side and the products (H + HF) on the lower energy, left hand side.]]<br />
The F + H<sub>2</sub> reaction is exothermic and the H + HF reaction is endothermic as the F + H<sub>2</sub> system lies on the higher energy side of the surface plot (Fig. 3) and H + HF on the lower energy side. This implies that the H-F bond is stronger than the H-H bond. The transition state is located at AB distance 1.808 and BC distance 0.751. This was identified as it was within the BC = 0.751 energy trough, and far enough along the AB separation that the system remained balanced at the transition state and did not slide to the products.<br />
The potential energy of the transition state is -103.538 kcal/mol, that of F + H<sub>2</sub> is -103.531 kcal/mol and that of H + HF is -132.539 kcal/mol. Therefore the activation energy for the formation of H + HF is +0.007 kcal/mol and the activation energy for the formation of F + H<sub>2</sub> is +29.001 kJ/mol.<br />
The reaction energy is released by the greater amplitude of vibration of the H-F product bond compared to the H-H reactant bond, therefore dissipating the energy to the surroundings through kinetic motion (Fig. 4), though the simulation doesn't show this eventual removal of energy from the system. This could be confirmed experimentally by measuring an increase in temperature during the reaction as energy is transferred to the surroundings by this increased amplitude of bond vibration.<br />
[[File:Momenta zohar.PNG|thumb|Fig. 4: Internuclear momenta for the reaction of F + H<sub>2</sub>, showing that the H + HF products have greater internuclear momenta than the reactants.]]<br />
[[File:Trajectory zohar.PNG|thumb|Fig. 5: Reactive trajectory from H + HF to F + H2]]<br />
A reactive trajectory is obtained with an AB distance of 0.92, BC distance of 2.23, AB momentum of -10 and BC momentum of -1 (Fig. 5). This relates to Polanyi's empirical rules, which state that kinetic/translational energy is ineffective in causing a system to cross a late transition state (i.e. that of the endothermic reaction of HF + H) and that only vibrational energy is effective in crossing such a barrier<ref><nowiki>http://brouard.chem.ox.ac.uk/teaching/dynlectures4to6.pdf (Accessed 10/05/2018)</nowiki></ref>. This leads to the release of energy by product translation rather than by product bond vibration, after the reaction has proceeded. The vibrational energy supplied is represented in the simulation as momentum between F and H, i.e. high amplitude vibration of the H-F reactant bond until it dissociates and the hydrogens collide and translate away from F.<br />
<br />
'''References'''</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=712580MRD:011967752018-05-11T13:53:21Z<p>Zm1116: </p>
<hr />
<div>[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
== EXERCISE 1: H + H<sub>2</sub> system ==<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|Reaction crosses over transition state and then returns to reactants, with vigorous oscillation<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|Reaction proceeds vigorously with movement over higher energy forms of the transition state on the way to the products<br />
|}<br />
'''Assumptions in transition state theory'''<br />
# The Born-Oppenheimer approximation is used, meaning that quantum tunnelling by electrons is not considered<ref name=":0"><nowiki>https://www.sciencedirect.com/topics/chemistry/transition-state-theory (accessed 08/05/2018)</nowiki></ref>. This means that motion along the reaction coordinate can be considered as a classical translation<ref name=":1">J. I. Steinfeld, J. S. Francisco, W. L. Hase, Chemical Kinetic and Dynamics, Prentice-Hall, United States, 1989</ref>.<br />
# The energies of the transition states which are reacting to form products follow the Boltzmann distribution, even when the reaction has not yet reached dynamic equilibrium<ref name=":1" />.<br />
# Once the transition state has been reached and there is momentum in the direction of the products, there will be no reversion to reactants<ref name=":0" />.<br />
These assumptions are however observed to be incorrect according to these simulations, as the fourth simulation shows the reactants crossing the transition state and then returning. Transition state theory would agree well with the experimental rate values for reactions which follow its assumptions, such as the first, second and third reactions, but would give poor approximations to the final two, especially as the fourth simulation breaks the third assumption of transition state theory.<br />
<br />
== EXERCISE 2: F - H - H system ==<br />
[[File:Transition state zohar.PNG|thumb|Fig. 3: Surface plot for the F + H<sub>2</sub> reaction, with the reactants (F + H<sub>2</sub>) on the higher energy, right hand side and the products (H + HF) on the lower energy, left hand side.]]<br />
The F + H<sub>2</sub> reaction is exothermic and the H + HF reaction is endothermic as the F + H<sub>2</sub> system lies on the higher energy side of the surface plot (Fig. 3) and H + HF on the lower energy side. This implies that the H-F bond is stronger than the H-H bond. The transition state is located at AB distance 1.808 and BC distance 0.751. This was identified as it was within the BC = 0.751 energy trough, and far enough along the AB separation that the system remained balanced at the transition state and did not slide to the products.<br />
The potential energy of the transition state is -103.538 kJ/mol, that of F + H<sub>2</sub> is -103.531 kJ/mol and that of H + HF is -132.539 kJ/mol. Therefore the activation energy for the formation of H + HF is +0.007 kJ/mol and the activation energy for the formation of F + H<sub>2</sub> is +29.001 kJ/mol.<br />
The reaction energy is released by the greater amplitude of vibration of the H-F product bond compared to the H-H reactant bond, therefore dissipating the energy to the surroundings through kinetic motion (Fig. 4), though the simulation doesn't show this eventual removal of energy from the system. This could be confirmed experimentally by measuring an increase in temperature during the reaction as energy is transferred to the surroundings by this increased amplitude of bond vibration.<br />
[[File:Momenta zohar.PNG|thumb|Fig. 4: Internuclear momenta for the reaction of F + H<sub>2</sub>, showing that the H + HF products have greater internuclear momenta than the reactants.]]<br />
[[File:Trajectory zohar.PNG|thumb|Fig. 5: Reactive trajectory from H + HF to F + H2]]<br />
A reactive trajectory is obtained with an AB distance of 0.92, BC distance of 2.23, AB momentum of -10 and BC momentum of -1 (Fig. 5). This relates to Polanyi's empirical rules, which state that kinetic/translational energy is ineffective in causing a system to cross a late transition state (i.e. that of the endothermic reaction of HF + H) and that only vibrational energy is effective in crossing such a barrier<ref><nowiki>http://brouard.chem.ox.ac.uk/teaching/dynlectures4to6.pdf (Accessed 10/05/2018)</nowiki></ref>. This leads to a release of energy by product translation rather than vibration. The vibrational energy supplied is represented in the simulation as momentum between F and H, i.e. high amplitude vibration of the reactant bond until it dissociates and the hydrogens collide and translate away from F.<br />
<br />
'''References'''</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=709989MRD:011967752018-05-10T16:34:47Z<p>Zm1116: </p>
<hr />
<div>== EXERCISE 1: H + H<sub>2</sub> system ==<br />
[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]<br />
<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|Reaction crosses over transition state and then returns to reactants, with vigorous oscillation<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|Reaction proceeds vigorously with movement over higher energy forms of the transition state on the way to the products<br />
|}<br />
'''Assumptions in transition state theory'''<br />
# The Born-Oppenheimer approximation is used, meaning that quantum tunnelling by electrons is not considered<ref name=":0"><nowiki>https://www.sciencedirect.com/topics/chemistry/transition-state-theory (accessed 08/05/2018)</nowiki></ref>. This means that motion along the reaction coordinate can be considered as a classical translation<ref name=":1">J. I. Steinfeld, J. S. Francisco, W. L. Hase, Chemical Kinetic and Dynamics, Prentice-Hall, United States, 1989</ref>.<br />
# The energies of the transition states which are reacting to form products follow the Boltzmann distribution, even when the reaction has not yet reached dynamic equilibrium<ref name=":1" />.<br />
# Once the transition state has been reached and there is momentum in the direction of the products, there will be no reversion to reactants<ref name=":0" />.<br />
These assumptions are however observed to be incorrect according to these simulations, as the fourth simulation shows the reactants crossing the transition state and then returning. Transition state theory would agree well with the experimental rate values for reactions which follow its assumptions, such as the first, second and third reactions, but would give poor approximations to the final two, especially as the fourth simulation breaks the third assumption of transition state theory.<br />
<br />
== EXERCISE 2: F - H - H system ==<br />
[[File:Transition state zohar.PNG|thumb|Fig. 3: Surface plot for the F + H<sub>2</sub> reaction, with the reactants (F + H<sub>2</sub>) on the higher energy, right hand side and the products (H + HF) on the lower energy, left hand side.]]<br />
The F + H<sub>2</sub> reaction is exothermic and the H + HF reaction is endothermic as the F + H<sub>2</sub> system lies on the higher energy side of the surface plot (Fig. 3) and H + HF on the lower energy side. This implies that the H-F bond is stronger than the H-H bond. The transition state is located at AB distance 1.808 and BC distance 0.751. This was identified as it was within the BC = 0.751 energy trough, and far enough along the AB separation that the system remained balanced at the transition state and did not slide to the products.<br />
The potential energy of the transition state is -103.538 kJ/mol, that of F + H<sub>2</sub> is -103.531 kJ/mol and that of H + HF is -132.539 kJ/mol. Therefore the activation energy for the formation of H + HF is +0.007 kJ/mol and the activation energy for the formation of F + H<sub>2</sub> is +29.001 kJ/mol.<br />
The reaction energy is released by the greater amplitude of vibration of the H-F product bond compared to the H-H reactant bond, therefore dissipating the energy to the surroundings through kinetic motion (Fig. 4), though the simulation doesn't show this eventual removal of energy from the system. This could be confirmed experimentally by measuring an increase in temperature during the reaction as energy is transferred to the surroundings by this increased amplitude of bond vibration.<br />
[[File:Momenta zohar.PNG|thumb|Fig. 4: Internuclear momenta for the reaction of F + H<sub>2</sub>, showing that the H + HF products have greater internuclear momenta than the reactants.]]<br />
[[File:Trajectory zohar.PNG|thumb|Fig. 5: Reactive trajectory from H + HF to F + H2]]<br />
A reactive trajectory is obtained with an AB distance of 0.92, BC distance of 2.23, AB momentum of -10 and BC momentum of -1 (Fig. 5). This relates to Polanyi's empirical rules, which state that kinetic/translational energy is ineffective in crossing a late transition state (i.e. that of an endothermic reaction) and that only vibrational energy is effective in crossing such a barrier<ref><nowiki>http://brouard.chem.ox.ac.uk/teaching/dynlectures4to6.pdf (Accessed 10/05/2018)</nowiki></ref>. This leads to a release of energy by product translation rather than vibration. The vibrational energy supplied is represented in the simulation as momentum between F and H, i.e. high amplitude vibration of the reactant bond until it dissociates and the hydrogens collide and translate away from F.<br />
<br />
'''References'''</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Trajectory_zohar.PNG&diff=709914File:Trajectory zohar.PNG2018-05-10T16:23:12Z<p>Zm1116: </p>
<hr />
<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Momenta_zohar.PNG&diff=709199File:Momenta zohar.PNG2018-05-10T14:46:55Z<p>Zm1116: </p>
<hr />
<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Transition_state_zohar.PNG&diff=708705File:Transition state zohar.PNG2018-05-10T13:54:21Z<p>Zm1116: </p>
<hr />
<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:F_%2B_H2_Zohar.PNG&diff=708386File:F + H2 Zohar.PNG2018-05-10T13:20:30Z<p>Zm1116: </p>
<hr />
<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=706881MRD:011967752018-05-08T17:15:34Z<p>Zm1116: </p>
<hr />
<div>== EXERCISE 1: H + H<sub>2</sub> system ==<br />
[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]<br />
<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|Reaction crosses over transition state and then returns to reactants, with vigorous oscillation<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|Reaction proceeds vigorously with movement over higher energy forms of the transition state on the way to the products<br />
|}<br />
'''Assumptions in transition state theory'''<br />
# The Born-Oppenheimer approximation is used, meaning that quantum tunnelling by electrons is not considered.<br />
# The reactant atom energies follow the Boltzmann distribution or are under thermal equilibrium<br />
# Once the transition state has been reached and there is momentum in the direction of the products, there will be no reversion to reactants.<ref><nowiki>https://www.sciencedirect.com/topics/chemistry/transition-state-theory (accessed 08/05/2018)</nowiki></ref><br />
These assumptions are however observed to be incorrect according to these simulations, as the fourth simulation shows the reactants crossing the transition state and then returning. Transition state theory would agree well with the experimental rate values for reactions which follow its assumptions, such as the first, second and third reactions, but would give poor approximations to the final two.</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=706694MRD:011967752018-05-08T16:03:44Z<p>Zm1116: </p>
<hr />
<div>[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]<br />
<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|<br />
|}</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=706688MRD:011967752018-05-08T16:03:09Z<p>Zm1116: </p>
<hr />
<div>[[File:Internuclear distance vs time Z.png|thumb|Fig. 1: Internuclear separation vs time]]<br />
'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>2</sub>: locating the transition state ====<br />
The best estimate of the transition state obtained in this investigation is r(ts) = 0.9077, as this results in minimal or no vibration of the atoms up and down the energy minimum curve on which the transition state rests. This can be seen from a plot of internuclear distances vs time (Fig. 1).<br />
<br />
==== Trajectories from r<sub>1</sub> = r<sub>ts</sub>+δ, r<sub>2</sub> = r<sub>ts</sub> ====<br />
The minimum energy path (mep) for an internuclear separation of r= r(ts) + 0.01 shows a smooth decrease in distance towards the transition state internuclear separation, as it does not account for momentum of atoms due to mass and velocity. The 'Dynamics' calculation does take these factors into account and therefore shows that when the atoms start off at a distance different to the transition state distance, they oscillate as they have been given momentum.<br />
[[File:Mep vs dynamics Z.PNG|thumb|600x600px|Fig. 2: Plots of the mep (left) and dynamics (right) calculations]]<br />
<br />
=== Reactive and unreactive trajectories ===<br />
For r1 = 0.74 and r2 = 2.0, an investigation was conducted into whether a series of combinations of momenta were reactive and what their total energy was.<br />
{| class="wikitable"<br />
!p1<br />
!p2<br />
!Total energy<br />
!Trajectory is reactive: Y/N<br />
!Plot<br />
!Description<br />
|-<br />
!-1.25<br />
!'''-2.5'''<br />
!-99.119<br />
!Y<br />
![[File:Plot 1 zms.PNG|thumb]]<br />
!Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|N<br />
|[[File:Plot 2 zms.PNG|thumb]]<br />
|Reactants approach transition state and do not have enough kinetic energy to cross the barrier, so revert to reactants<br />
|-<br />
|<nowiki>-1.5</nowiki><br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 3 zms.PNG|thumb]]<br />
|Reaction proceeds with normal oscillation from reactants to products<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.0</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Overall unreactive<br />
|[[File:Plot 4 zms.PNG|thumb]]<br />
|<br />
|-<br />
|<nowiki>-2.5</nowiki><br />
|<nowiki>-5.2</nowiki><br />
|<nowiki>-99.119</nowiki><br />
|Y<br />
|[[File:Plot 5 zms.PNG|thumb]]<br />
|<br />
|}</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Plot_5_zms.PNG&diff=706347File:Plot 5 zms.PNG2018-05-08T15:32:04Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Plot_4_zms.PNG&diff=706344File:Plot 4 zms.PNG2018-05-08T15:31:54Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Plot_3_zms.PNG&diff=706343File:Plot 3 zms.PNG2018-05-08T15:31:44Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Plot_2_zms.PNG&diff=706339File:Plot 2 zms.PNG2018-05-08T15:31:35Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Plot_1_zms.PNG&diff=706338File:Plot 1 zms.PNG2018-05-08T15:31:19Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Mep_vs_dynamics_Z.PNG&diff=705923File:Mep vs dynamics Z.PNG2018-05-08T14:57:34Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:Internuclear_distance_vs_time_Z.png&diff=705756File:Internuclear distance vs time Z.png2018-05-08T14:42:51Z<p>Zm1116: </p>
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<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=MRD:01196775&diff=705462MRD:011967752018-05-08T14:12:01Z<p>Zm1116: Created page with "'''Dynamics from the transition state region''' At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zer..."</p>
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<div>'''Dynamics from the transition state region'''<br />
<br />
At a minimum, the first derivative of the graph ∂V(r1)/∂r1 is equal to zero, and the second derivative is larger than zero, implying an increasing curvature around the minimum. At a transition state, the first derivative is equal to zero and the second derivative is smaller than zero, implying that it represents a maximum in energy as the curvature leading up to it is decreasing.</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611798Rep:Mod:011967752017-03-24T12:19:36Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 molecule ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the structure of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
<br />
There was an optimised C-F bond length of 1.32423 Å<ref name= "tfebonds"/> compared with a literature range of 1.311–1.321 Å, which the optimised value is just above. The optimised C=C bond length of 1.32540 Å was compared with the literature value of 1.337 Å<ref name= "tfebonds"/>, a close agreement.<br />
<br />
The optimised F-C-F bond angle was 113.716°, compared with the literature value of 104.35°<ref name= "tfebonds"/>. This agreement was less close and could have been more strongly influenced by differences in assumed conditions when modelling versus in the real experiment, including medium and temperature.<br />
<br />
The charge on both the carbon atoms was 0.631 and on all the fluorines was -0.315 as the molecule is symmetrical and fluorine is more electronegative than carbon, therefore drawing electron density towards itself in each C-F bond.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
<br />
<ref name="tfebonds"> D. Lentz, A. Bach, J. Buschmann, P. Luger and M. Messerschmidt, ''Chem. Eur. J.'', 2004, '''10''', 5059 - 5066.</ref><br />
<br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611789Rep:Mod:011967752017-03-24T12:17:01Z<p>Zm1116: /* N2 molecule */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the structure of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
<br />
There was an optimised C-F bond length of 1.32423 Å<ref name= "tfebonds"/> compared with a literature range of 1.311–1.321 Å, which the optimised value is just above. The optimised C=C bond length of 1.32540 Å was compared with the literature value of 1.337 Å<ref name= "tfebonds"/>, a close agreement.<br />
<br />
The optimised F-C-F bond angle was 113.716°, compared with the literature value of 104.35°<ref name= "tfebonds"/>. This agreement was less close and could have been more strongly influenced by differences in assumed conditions when modelling versus in the real experiment, including medium and temperature.<br />
<br />
The charge on both the carbon atoms was 0.631 and on all the fluorines was -0.315 as the molecule is symmetrical and fluorine is more electronegative than carbon, therefore drawing electron density towards itself in each C-F bond.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
<br />
<ref name="tfebonds"> D. Lentz, A. Bach, J. Buschmann, P. Luger and M. Messerschmidt, ''Chem. Eur. J.'', 2004, '''10''', 5059 - 5066.</ref><br />
<br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611786Rep:Mod:011967752017-03-24T12:15:03Z<p>Zm1116: /* Tetrafluoroethene: the monomer of PTFE */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the structure of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
<br />
There was an optimised C-F bond length of 1.32423 Å<ref name= "tfebonds"/> compared with a literature range of 1.311–1.321 Å, which the optimised value is just above. The optimised C=C bond length of 1.32540 Å was compared with the literature value of 1.337 Å<ref name= "tfebonds"/>, a close agreement.<br />
<br />
The optimised F-C-F bond angle was 113.716°, compared with the literature value of 104.35°<ref name= "tfebonds"/>. This agreement was less close and could have been more strongly influenced by differences in assumed conditions when modelling versus in the real experiment, including medium and temperature.<br />
<br />
The charge on both the carbon atoms was 0.631 and on all the fluorines was -0.315 as the molecule is symmetrical and fluorine is more electronegative than carbon, therefore drawing electron density towards itself in each C-F bond.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
<br />
<ref name="tfebonds"> D. Lentz, A. Bach, J. Buschmann, P. Luger and M. Messerschmidt, ''Chem. Eur. J.'', 2004, '''10''', 5059 - 5066.</ref><br />
<br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611769Rep:Mod:011967752017-03-24T12:10:40Z<p>Zm1116: /* Tetrafluoroethene: the monomer of PTFE */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the structure of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
<br />
There was an optimised C-F bond length of 1.32423 Å<ref name= "tfebonds"/> compared with a literature range of 1.311–1.321 Å, which the optimised value is just above. The optimised C=C bond length of 1.32540 Å was compared with the literature value of 1.337 Å<ref name= "tfebonds"/>, a close agreement.<br />
<br />
The optimised F-C-F bond angle was 113.716°, compared with the literature value of 104.35°<ref name= "tfebonds"/>. This agreement was less close and could have been more strongly influenced by differences in assumed conditions when modelling versus in the real experiment, including medium and temperature.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
<br />
<ref name="tfebonds"> D. Lentz, A. Bach, J. Buschmann, P. Luger and M. Messerschmidt, ''Chem. Eur. J.'', 2004, '''10''', 5059 - 5066.</ref><br />
<br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611762Rep:Mod:011967752017-03-24T12:08:45Z<p>Zm1116: /* References */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the structure of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
<br />
There was an optimised C-F bond length of 1.32423 Å<ref name= "tfebonds"/ compared with a literature range of 1.311–1.321 Å, which the optimised value is just above.<br />
<br />
The optimised C=C bond length of 1.32540 Å was compared with the literature value of 1.337 Å<ref name= "tfebonds"/>, a close agreement.<br />
<br />
The optimised F-C-F bond angle was 113.716°, compared with the literature value of 104.35°<ref name= "tfebonds"/>.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
<br />
<ref name="tfebonds"> D. Lentz, A. Bach, J. Buschmann, P. Luger and M. Messerschmidt, ''Chem. Eur. J.'', 2004, '''10''', 5059 - 5066.</ref><br />
<br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611745Rep:Mod:011967752017-03-24T12:05:28Z<p>Zm1116: /* Tetrafluoroethene: the monomer of PTFE */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the structure of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
<br />
There was an optimised C-F bond length of 1.32423 Å<ref name= "tfebonds"/ compared with a literature range of 1.311–1.321 Å, which the optimised value is just above.<br />
<br />
The optimised C=C bond length of 1.32540 Å was compared with the literature value of 1.337 Å<ref name= "tfebonds"/>, a close agreement.<br />
<br />
The optimised F-C-F bond angle was 113.716°, compared with the literature value of 104.35°<ref name= "tfebonds"/>.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611686Rep:Mod:011967752017-03-24T11:46:14Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines. This MO is the reason why π bonding is not observed in this molecule, as it consists of multiple π* orbitals. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611666Rep:Mod:011967752017-03-24T11:43:54Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143 Å with the middle fluorine, compared with literature values of 1.698 Å and 1.598 Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement. This angle is not 90° as in a typical trigonal bipyramidal structure as the two lone pairs repel the bonding pairs by a greater degree than a pair of bonding electrons would have.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684 Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, while the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle Cl-F bonding pair experiences less electronic repulsion, as it has a greater angle between it and the lone pairs than the outer fluorines do. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all Cl-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611632Rep:Mod:011967752017-03-24T11:36:42Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143Å with the middle fluorine, compared with literature values of 1.698Å and 1.598Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values (all three Cl-F bonds were of length 1.75684Å) and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611620Rep:Mod:011967752017-03-24T11:34:23Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143Å with the middle fluorine, compared with literature values of 1.698Å and 1.598Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°, compared with a literature value of 87.29°<ref name="clf3bonds" />, a very close agreement.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611617Rep:Mod:011967752017-03-24T11:34:01Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143Å with the middle fluorine, compared with literature values of 1.698Å and 1.598Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
The optimised F-Cl-F bond angle was 87.140°<ref name="clf3bonds" />, compared with a literature value of 87.29°, a very close agreement.<br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611602Rep:Mod:011967752017-03-24T11:31:48Z<p>Zm1116: /* References */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143Å with the middle fluorine, compared with literature values of 1.698Å and 1.598Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
F-Cl-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
<br />
<ref name="clf3bonds">D.F. Smith, ''J. Chem. Phys.'', 1953, '''21'''(4), 609–614.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611591Rep:Mod:011967752017-03-24T11:29:05Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143Å with the middle fluorine, compared with literature values of 1.698Å and 1.598Å<ref name="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
F-Cl-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611588Rep:Mod:011967752017-03-24T11:28:43Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond lengths were 1.72863 Å with the outer fluorines and 1.65143Å with the middle fluorine, compared with literature values of 1.698Å and 1.598Å<refname="clf3bonds" />, which is a fairly good agreement; again, electronegativity making the bonding have a small degree of ionic character is likely the cause.<br />
<br />
F-Cl-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611560Rep:Mod:011967752017-03-24T11:23:35Z<p>Zm1116: /* ClF3 */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
Optimised Cl-F bond length was 1.72863 Å compared with literature values of 1.598 Å and 1.698 Å<br />
<br />
F-Cl-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611524Rep:Mod:011967752017-03-24T11:17:02Z<p>Zm1116: /* Energy changes associated with the Haber-Bosch process */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as the compounding of small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611520Rep:Mod:011967752017-03-24T11:15:36Z<p>Zm1116: /* Energy changes associated with the Haber-Bosch process */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and in the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature, as well as small discrepancies in real and calculated bond lengths and angles.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611514Rep:Mod:011967752017-03-24T11:13:29Z<p>Zm1116: /* NH3 molecule */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. This could be due to a small discrepancy in modelled electron density versus in real conditions.<br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611503Rep:Mod:011967752017-03-24T11:11:59Z<p>Zm1116: /* NH3 molecule */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008Å<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure. <br />
<br />
The optimised H-N-H bond angle was 105.741°, compared with a literature value of 107.298°<ref name="nhbond"/>. <br />
<br />
Despite small differences, the calculated values for bond length and angle are a close fit to the literature values, implying that Gaussview is able to very accurately model these molecules. Therefore, energy calculations based on this are likely to be accurate for the conditions under which the molecule is modelled.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611486Rep:Mod:011967752017-03-24T11:04:50Z<p>Zm1116: /* Energy changes associated with the Haber-Bosch process */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure.<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value. This difference can be attributed to a difference in the conditions at which the experiment was conducted, such as the medium and temperature.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611474Rep:Mod:011967752017-03-24T11:00:27Z<p>Zm1116: /* References */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure.<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<br />
<ref name="nhbond">''Table of Interatomic Distances and Configuration of Molecules and Ions'', Special Publication No 11; Supplement 1956–1959, Special Publication No 18, Chemical Society, London, 1958, 1965.</ref><br />
<br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611465Rep:Mod:011967752017-03-24T10:57:49Z<p>Zm1116: /* NH3 molecule */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
The optimised N-H bond length was 1.01798 Å, in contrast with a literature value of 1.008<ref name="nhbond"/>, a difference likely due to the fact that electronegativity differences between nitrogen and hydrogen mean that the bond has some ionic character and is therefore slightly shorter and stronger than can be predicted by an optimisation based on a completely covalent structure.<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611383Rep:Mod:011967752017-03-24T10:46:40Z<p>Zm1116: /* Tetrafluoroethene: the monomer of PTFE */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised TFE</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS TFE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS TFE OPTF POP.LOG| here]]<br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
==References==<br />
<br />
<references><br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=File:ZOHARMS_TFE_OPTF_POP.LOG&diff=611376File:ZOHARMS TFE OPTF POP.LOG2017-03-24T10:45:43Z<p>Zm1116: </p>
<hr />
<div></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611361Rep:Mod:011967752017-03-24T10:43:22Z<p>Zm1116: /* Energy changes associated with the Haber-Bosch process */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol calculated for the formation of 2NH3, so the calculated enthalpy of formation of ammonia is -73.239247005kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJ/mol<ref name="nh3formation" />, showing a significant difference between the calculated value and the actual value.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
<br />
==References==<br />
<br />
<references><br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611337Rep:Mod:011967752017-03-24T10:39:43Z<p>Zm1116: /* References */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJmol-1<ref name="nh3formation" /><br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
<br />
==References==<br />
<br />
<references><br />
<ref name="nh3formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274.</ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611332Rep:Mod:011967752017-03-24T10:38:35Z<p>Zm1116: /* Tetrafluoroethene: the monomer of PTFE */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJmol-1<ref name="nh3formation" /><br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.<br />
<br />
<br />
==References==<br />
<br />
<references><br />
<ref name="nh3 formation">M. Sana, G. Leroy, D. Peeters and C. Wilante, ''J. Mol. Struct.'', 1988, '''164''', 249-274 </ref><br />
</references></div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611303Rep:Mod:011967752017-03-24T10:32:14Z<p>Zm1116: /* Energy changes associated with the Haber-Bosch process */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol. The literature value for the enthalpy of formation of ammonia is -45.910 kJmol-1<ref name="nh3formation" /><br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611267Rep:Mod:011967752017-03-24T10:22:14Z<p>Zm1116: /* NH3 molecule */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|400px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.</div>Zm1116https://chemwiki.ch.ic.ac.uk/index.php?title=Rep:Mod:01196775&diff=611266Rep:Mod:011967752017-03-24T10:21:53Z<p>Zm1116: /* NH3 molecule */</p>
<hr />
<div>== NH3 molecule==<br />
<br />
<pre><br />
nh3 optimisation<br />
File Name ZoharMS_nh3_optf_pop<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -56.55776873 a.u.<br />
RMS Gradient Norm 0.00000485 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 1.8466 Debye<br />
Point Group C3V<br />
Job cpu time: 0 days 0 hours 0 minutes 9.0 seconds.<br />
</pre><br />
<br />
Optimised N-H bond length: 1.01798 Å<br />
<br />
Optimised H-N-H bond angle: 105.741° <br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000004 0.000450 YES<br />
RMS Force 0.000004 0.000300 YES<br />
Maximum Displacement 0.000072 0.001800 YES<br />
RMS Displacement 0.000035 0.001200 YES<br />
Predicted change in Energy=-5.986298D-10<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.018 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.018 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.018 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 105.7412 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 105.7412 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 105.7412 -DE/DX = 0.0 !<br />
! D1 D(2,1,4,3) -111.8571 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised NH3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS NH3 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS NH3 OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS NH3 display vibrations2.PNG|600px]]<br />
<br />
From the 3N-6 rule, 6 vibrations were expected and subsequently calculated.<br />
<br />
Modes 2 & 3 as well as 5 & 6 are degenerate, due to their having the same IR frequency, and therefore the same energy as frequency is proportional to energy by the de Broglie relationship. Modes 1, 2, 3 are bending vibrations while 4, 5, 6 are bond stretching vibrations. Mode 4 is highly symmetric as all the N-H bonds contract and extend in unison. Mode 1 is an umbrella mode since the N-H bonds move upwards around the nitrogen atom like an umbrella opening.<br />
<br />
[[File:ZoharMS nh3 spectrum.PNG|400px]]<br />
<br />
In an experimental IR spectrum of gaseous ammonia, one could expect to see 2 bands as only three of the vibrations (1,2,3) have a change in dipole moment and therefore a high enough intensity on IR to be visible, and two of these (2,3) are degenerate and thus will only produce a single band.<br />
<br />
There is a charge of -1.125 on nitrogen and +0.375 on each of the hydrogens. This is as expected as nitrogen is more electronegative than hydrogen, so it will usually hold bonding electrons more tightly than hydrogen in an N-H bond. Additionally, there is a lone pair of electrons on nitrogen with a significant negative charge.<br />
<br />
==N2 molecule==<br />
<br />
<pre><br />
n2 optimisation<br />
File Name ZoharMS_n2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -109.52412868 a.u.<br />
RMS Gradient Norm 0.00000365 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 1.10550 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000006 0.000450 YES<br />
RMS Force 0.000006 0.000300 YES<br />
Maximum Displacement 0.000002 0.001800 YES<br />
RMS Displacement 0.000003 0.001200 YES<br />
Predicted change in Energy=-1.248809D-11<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.1055 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised N2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS N2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is liked to [[Media:ZOHARMS N2 OPTF POP.LOG| here]]<br />
<br />
As can be seen below, N2 has only one mode with an IR spectrum of intensity 0. This is due to the fact that charge is equally distributed between both nitrogens; therefore no dipole is present and no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS N2 display vibrations.png|800px]]<br />
<br />
==H2 molecule==<br />
<pre><br />
h2 optimisation<br />
File Name ZoharMS_h2_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -1.17853936 a.u.<br />
RMS Gradient Norm 0.00000017 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.0000 Debye<br />
Point Group D∞h<br />
</pre><br />
<br />
Bond length: 0.74279 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000000 0.000450 YES<br />
RMS Force 0.000000 0.000300 YES<br />
Maximum Displacement 0.000000 0.001800 YES<br />
RMS Displacement 0.000001 0.001200 YES<br />
Predicted change in Energy=-1.164080D-13<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 0.7428 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<br />
<jmol><jmolApplet><br />
<title>optimised H2</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS H2 OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS H2 OPTF POP.LOG| here]]<br />
<br />
H2 produces a blank IR spectrum for the same reasons as N2 does: it is homonuclear and so no change in dipole moment is possible.<br />
<br />
[[File:ZoharMS H2 display vibrations.png|800px]]<br />
<br />
== Energy changes associated with the Haber-Bosch process ==<br />
<br />
The Haber-Bosch process is an important chemical process by which ammonia is formed artificially from nitrogen and hydrogen gases. It is carried out on a massive scale globally as it provides a significant proportion of the ammonia used in fertilisers, and has therefore enabled the production of sufficient food for the growing global population. The energy associated with this process is important as it is quite energy intensive and understanding the energy associated with this exothermic reaction can aid in the design of reactors in which to carry out the process, and the design of industrial reaction conditions.<br />
<br />
Energies of each of these molecules were obtained by optimisation in Gaussview 5.0, and analysed in the following manner in hartree units:<br />
<br />
E(NH3)= -56.55776873<br />
<br />
2*E(NH3)= -113.11553746<br />
<br />
E(N2)= -109.52412868<br />
<br />
E(H2)= -1.17853936<br />
<br />
3*E(H2)= -3.53561808<br />
<br />
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907<br />
<br />
This is equivalent to a ΔE of -146.47849401 kJ/mol.<br />
<br />
== ClF3 ==<br />
<br />
<pre><br />
ClF3 T shape optimisation<br />
File Name ZoharMs_ClF3_Tshape_optf_pop<br />
File Type .chk<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(D,P)<br />
Charge 0<br />
Spin Singlet<br />
Total Energy -759.46531688 a.u.<br />
RMS Gradient Norm 0.00002465 a.u.<br />
Imaginary Freq<br />
Dipole Moment 0.8386 Debye<br />
Point Group<br />
</pre><br />
<br />
C-F bond length: 1.72863 Å<br />
<br />
F-C-F bond angle: 87.140° <br />
<br />
Originally these values were optimised for a ClF3 molecule in a trigonal planar structure, but the results were significantly different to the literature values and so an alternative T-shape structure for three bonding pairs and two lone pairs was investigated, which gave much better agreement with the literature values.<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000050 0.000450 YES<br />
RMS Force 0.000028 0.000300 YES<br />
Maximum Displacement 0.000204 0.001800 YES<br />
RMS Displacement 0.000134 0.001200 YES<br />
Predicted change in Energy=-1.250234D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.6514 -DE/DX = 0.0 !<br />
! R2 R(1,3) 1.7286 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.7286 -DE/DX = 0.0 !<br />
! A1 A(2,1,3) 87.1404 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 87.1404 -DE/DX = 0.0 !<br />
! A3 L(3,1,4,2,-1) 174.2807 -DE/DX = 0.0 !<br />
! A4 L(3,1,4,2,-2) 180.0 -DE/DX = 0.0 !<br />
! D1 D(1,2,4,3) 0.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
<jmol><jmolApplet><br />
<title>optimised ClF3</title><br />
<color>black</color><br />
<size>400</size><br />
<uploadedFileContents>ZOHARMS CLF3 TSHAPE OPTF POP.LOG</uploadedFileContents><br />
</jmolApplet></jmol><br />
<br />
The optimisation file is linked to [[Media:ZOHARMS CLF3 TSHAPE OPTF POP.LOG| here]]<br />
<br />
[[File:ZoharMS ClF3 display vibrations.png|800px]]<br />
<br />
The charge on chlorine is +1.225 and that on the two outermost fluorine atoms is -0.454, and the charge on the fluorine in the middle of the T shape is -0.316. Fluorine carries a negative charge and chlorine a positive charge as fluorine is more electronegative and polarizes electron density towards itself. The middle fluorine is not as negatively charged as the other two as the pseudostructure is trigonal bipyramidal and the middle C-F bond's electron density is diverted towards the two lone pairs also in the trigonal section. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 2.PNG|400px]]<br />
<br />
<br />
This is the lowest energy bonding MO, and its contributing AOs are 2s on chlorine and 2s on all three fluorine atoms. It is relatively deep in energy (-1.28161), it is occupied and it contributes roughly homogenous electron density across all four atoms. This is the lowest energy MO despite being made up of 2s orbitals as the 1s orbitals are too low in energy and are therefore non-bonding. <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 5.PNG|400px]]<br />
<br />
This is a part-bonding, part-antibonding occupied orbital deep in energy (-1.17368) with all contributions coming from 2s AOs. Its effect is to increase electron density between chlorine and the two peripheral fluorines as it will undergo positive interference with the first MO shown here. It also decreases electron density between chlorine and the middle fluorine due to the node present between them.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 6.PNG|400px]]<br />
<br />
This is a bonding, occupied MO below the HOMO/LUMO region in energy (-0.53818), with electron density contributed by 2p AOs on all atoms. It has electron density above and below the plane of the molecule but not within it, implying some π character (though a later π* orbital must cancel this out as the overall bonding in the molecule is primarily σ). <br />
<br />
<br />
[[File:ZoharMS ClF3 MO 4.PNG|400px]]<br />
<br />
<br />
This is the HOMO and therefore its energy is in the HOMO/LUMO region (-0.33458). It is occupied but antibonding as it can be seen that it consists of 2p orbitals on each of the atoms which are perpendicular to the plane of the molecule, which are all out of phase with each other. It is interesting to note the smaller 2p orbital size on the middle fluorine, which earlier was shown to have a less negative charge than the other two fluorines.<br />
<br />
<br />
[[File:ZoharMS ClF3 MO 3.PNG|400px]]<br />
<br />
<br />
This is an antibonding LUMO made up of 2p orbitals on chlorine and all three fluorines, therefore it is unoccupied. These 2p orbitals are involved in creating the σ* orbitals, and therefore lie in the plane of the molecule. It can be seen that it is completely antibonding as there is a node across each bond in the molecule. Its energy is in the HOMO/LUMO region (-0.15086) and if it is occupied, this will cause all C-F bonds to break.<br />
<br />
==Tetrafluoroethene: the monomer of PTFE==<br />
<br />
Polytetrafluoroethene (PTFE) is a material with very low friction and is therefore useful for coating pans to make them non-stick. It is a polymer of tetrafluoroethene (TFE) monomers and so understanding the energy requirements for synthesising TFE is useful for industry. The following is an investigation of the energy of TFE.<br />
<br />
<pre><br />
TFE optimisation<br />
File Name ZOHARMS_TFE_OPTF_POP<br />
File Type .log<br />
Calculation Type FREQ<br />
Calculation Method RB3LYP<br />
Basis Set 6-31G(d,p)<br />
Charge 0<br />
Spin Singlet<br />
E(RB3LYP) -475.49961623 a.u.<br />
RMS Gradient Norm 0.00006120 a.u.<br />
Imaginary Freq 0<br />
Dipole Moment 0.0000 Debye<br />
Point Group C2H<br />
Job cpu time: 0 days 0 hours 0 minutes 22.0 seconds.<br />
</pre><br />
<br />
C-F bond length: 1.32423 Å<br />
<br />
C=C bond length: 1.32540 Å<br />
<br />
<pre><br />
Item Value Threshold Converged?<br />
Maximum Force 0.000206 0.000450 YES<br />
RMS Force 0.000067 0.000300 YES<br />
Maximum Displacement 0.000222 0.001800 YES<br />
RMS Displacement 0.000146 0.001200 YES<br />
Predicted change in Energy=-5.785176D-08<br />
Optimization completed.<br />
-- Stationary point found.<br />
----------------------------<br />
! Optimized Parameters !<br />
! (Angstroms and Degrees) !<br />
-------------------------- --------------------------<br />
! Name Definition Value Derivative Info. !<br />
--------------------------------------------------------------------------------<br />
! R1 R(1,2) 1.3254 -DE/DX = 0.0002 !<br />
! R2 R(1,3) 1.3242 -DE/DX = 0.0 !<br />
! R3 R(1,4) 1.3241 -DE/DX = 0.0001 !<br />
! R4 R(2,5) 1.3242 -DE/DX = 0.0 !<br />
! R5 R(2,6) 1.3241 -DE/DX = 0.0001 !<br />
! A1 A(2,1,3) 123.1336 -DE/DX = 0.0 !<br />
! A2 A(2,1,4) 123.1507 -DE/DX = 0.0 !<br />
! A3 A(3,1,4) 113.7158 -DE/DX = 0.0 !<br />
! A4 A(1,2,5) 123.1336 -DE/DX = 0.0 !<br />
! A5 A(1,2,6) 123.1507 -DE/DX = 0.0 !<br />
! A6 A(5,2,6) 113.7158 -DE/DX = 0.0 !<br />
! D1 D(3,1,2,5) 180.0 -DE/DX = 0.0 !<br />
! D2 D(3,1,2,6) 0.0 -DE/DX = 0.0 !<br />
! D3 D(4,1,2,5) 0.0 -DE/DX = 0.0 !<br />
! D4 D(4,1,2,6) 180.0 -DE/DX = 0.0 !<br />
--------------------------------------------------------------------------------<br />
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad<br />
</pre><br />
<br />
The IR spectrum frequencies are shown below. As can be seen from the intensities, one could expect two peaks in the diagnostic region as the rest of the vibrations either have no change in dipole or only a small change in dipole which would produce extremely small peaks.<br />
<br />
[[File:ZoharMS TFE display vibrations.PNG|400 px]]<br />
<br />
[[File:ZoharMS tfe spectrum.PNG|400 px]]<br />
<br />
Below, two molecular orbitals are investigated: the HOMO and LUMO of TFE. The LUMO is of particular interest as it is the interactions between the LUMOs of multiple TFE monomers which cause them to react to form PTFE.<br />
<br />
[[File:ZoharMS tfe mo 1.PNG|400 px]]<br />
<br />
This is the HOMO with an energy of -0.25422. It has both bonding and antibonding character and is the final filled orbital, which serves to increase electron density in the C=C π bond above and below the plane of the molecule by positive interference with lower energy orbitals which also have bonding character between the carbon atoms. It also reduces electron density between each carbon and fluorine due to the presence of a node in the C-F bonds. It is made up of the 2p orbital perpendicular to the plane of the molecule on each atom, and is therefore unaffected by the sp2 hybridisation of carbon (the hybrid orbitals lie in the plane of the molecule).<br />
<br />
[[File:ZoharMS tfe mo 2.PNG|400 px]]<br />
<br />
This is the LUMO. It is similar to the HOMO in terms of which AOs are involved, but its energy is positive (0.03000) and it is completely antibonding. The electron density on each fluorine is smaller than that in the HOMO implying slightly weaker antibonding character in the C-F bond, but importantly there is a node between the two carbon atoms representing the antibonding C=C π*. If electron density is donated into this LUMO by another TFE molecule, the negative interference between the HOMO (C=C π) and LUMO (C=C π*) causes the C=C π bond to break and only the C-C σ bond remains. The electrons now enter two new C-C σ bonds with neighbouring monomers to form the polymer.</div>Zm1116