ChemWiki - User contributions [en]

CP3MD

2016-04-25T15:25:04Z

Mjbear: /* Dynamics computation from the TS: Release of the energy of exothermicity */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''Discussion''': What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet to structure your results and brief discussion. Explain why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.  

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of energy ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-25T15:22:40Z

Mjbear: /* Discussion of the first part of the exercise */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''Discussion''': What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet to structure your results and brief discussion. Explain why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.  

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-25T15:21:55Z

Mjbear: /* Discussion of the first part of the exercise */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''Discussion''': What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Explain why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.  

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-25T15:20:03Z

Mjbear: /* Guidance on your report for Part 1: the H and H2 system */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''Discussion''': What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.  

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-25T15:19:11Z

Mjbear: /* Guidance on your report for Part 1: the H and H2 system */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''Discussion''': What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
/* Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.  

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction. */

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.  

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-25T15:18:11Z

Mjbear: /* Generating reactive trajectories */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''Discussion''': What value does the total gradient of the potential energy surface have at a minimum and at a transition structure? Briefly explain how minima and transition structures can be distinguished using the curvature of the potential energy surface.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T18:26:54Z

Mjbear: /* Background reading */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T16:36:39Z

Mjbear: /* Background reading */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6 Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T16:02:44Z

Mjbear: /* The software */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

Chemistry computer rooms have been booked for the 2nd year computational exercises when they are running this term, and demonstrators will be available on the days these are timetabled for.

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T15:58:50Z

Mjbear: /* The write-up Required */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

Submit your completed data sheet via Blackboard by 6 pm on the Friday in the week you carry out the exercise.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T15:47:35Z

Mjbear: /* Dynamics computation from the TS: Release of the energy of exothermicity */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of energy in this reaction?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T15:42:35Z

Mjbear: /* The write-up Required */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated.

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-22T15:41:44Z

Mjbear: /* The write-up Required */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available [[:File:Data sheet template v2.docx|here]].

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

It is possible to simulate a chemical reaction by describing the relative motion of the atoms that occurs while the reaction takes place. Since the mass of the atoms is relatively large (compare with the mass of the electron for example), for many chemical reactions it is possible to assume that the motion of the atoms follow Newton's equations of motion, i.e. obey classical mechanics. This is an approximation, since it neglects the fact that molecular vibrations are quantized or quantum tunneling effects, but it is nevertheless a good approximation for most chemical reactions.

The relative motion of the atoms will depend on the interaction between them, which in turn depends on their relative position (for example, how far their nuclei are from each other). Interatomic interactions, as part of a molecule or not, are expressed as a ''potential energy surface'' '''V(r)''' which represent the potential energy of the system as a function of the atoms' relative positions defined by the general vector '''r'''. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy and eventually to dissociation).

The force (variation of momentum '''p''') acting on a given interatomic coordinate '''ri''' will depend on the derivative of the potential energy surface with respect to that coordinate.

<math> {dp_i \over dt} = - { \partial V(r_1,r_2,...)\over \partial r_i}</math>

By solving the equations of motion we are able to determine the trajectory of the system, i.e. determine the relative position of the atoms at each instant in time '''r'''(t). The trajectory represents a path across the potential energy surface (you will see examples shortly), and can be used to gain insight on how the reaction might proceed.

Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.80 '''and '''r2 '''(FH-H) = '''0.75'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS ===
Set the momenta to '''p1 '''= '''0''' and''' p2 '''= '''0''' and offset the distances from the TS to '''r1''' = '''1.78''',''' r2''' = '''0.75'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. Note:''' You will need a large number of steps (>10000) to reach the valley floor.

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

File:Data sheet template v2.docx

2016-04-22T15:40:03Z

Mjbear: Template for writing up 2nd year Molecular Dynamics version (from 2016)

Template for writing up 2nd year Molecular Dynamics version (from 2016)

CP3MD

2016-04-20T16:29:31Z

Mjbear: /* EXERCISE 2: F + H2 system */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde. Updated for 2016 by Tristan Mackenzie, Nathan Fitzpatrick, Dr João Malhado and Prof Michael Bearpark''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed. [MB suggest leaving this]'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T16:13:57Z

Mjbear: /* Dynamics from the transition state region */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde.''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''Up to this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed. [MB suggest leaving this]'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value on the data sheet.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. Convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use. '''''Write these down on the data sheet.'''''
Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between 0.8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5
==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet and describe what happens.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1: the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment, including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. Expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T15:59:40Z

Mjbear: /* EXERCISE 1: H + H2 system */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde.''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer. ''Please do not rush through this part of the exercise, as it is designed to develop your understanding of potential energy surfaces, reaction coordinates, transition structures, and to introduce the difference between kinetics and dynamics which can be studied experimentally.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

Up to''''' this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed. [MB suggest leaving this]'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T15:57:14Z

Mjbear: /* Dynamics from the transition state region */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde.''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer.''

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

Up to''''' this point, you have been learning how to use the program to visualise a triatomic reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed. [MB suggest leaving this]'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T15:46:09Z

Mjbear: /* Molecular Reaction Dynamics: Applications to Triatomic systems */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Dr Paul Wilde.''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in Figure 2. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In Figure 2, the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer.''

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see [[Running MD code in MATLAB|instructions]]). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.

* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.

* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 4: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 5: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 6: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in Figure 7.

[[File:Y2C10.png|thumb|500px|left|'''Figure 7: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 8: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 9 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 9: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:56:43Z

Mjbear: /* Dynamics from the transition state region */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. ''They do not form part of the assessed work directly, but there are questions on the data sheet / writeup template to answer.''

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:52:23Z

Mjbear: /* EXERCISE 1: H + H2 system */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactant and product channels. Observe how the line is wavy: this indicates that the diatomic molecule is vibrating. The most important point to observe is conservation of energy: the system will always oscillate between energy contours with the same value.
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the product / exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly).
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as shown by the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as the '''''maximum''' ''on the '''''minimum energy path''''' linking reactants and the products. This point on the potential energy surface has the special property that dV('''r''')/d'''r''' (the gradient of the potential) is zero, and the energy goes down most steeply along the minimum energy path linking reactants and products. Consequently, if one starts a trajectory exactly at the transition state, with no initial momentum, it will remain there forever. However, if one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always reset to zero). Once the transition state has been located, one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:42:01Z

Mjbear: /* EXERCISE 1: H + H2 system */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are currently labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in both forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of the AB or BC distances you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:39:55Z

Mjbear:

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2, '''and the products ('''r1''' small '''r2''' large). (Note that the variation of potential energy along the combined r2 and r1 axes is the typical curve you have seen before). The general triatomic system depicted means we started with atom A and molecule BC and ended with molecule AB and atom C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to product; not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier or its surroundings and regenerate the reactants.

For a given potential surface, the outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)).

''Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even, if one has enough energy to surmount the barrier.''

In the program you will use, you will run trajectories on different potential surfaces - corresponding to different triatomic chemical systems - for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will first study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:34:35Z

Mjbear: /* Atom-Diatom Collisions */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2, while m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be approximately constant (it will oscillate slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be approximately constant (but it will oscillate slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a '''potential energy surface''' where potential energy is plotted as a function of both r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2 '''and the products ('''r1''' small '''r2''' large). (You may note that the variation of PE along the r2 and r1 axes is the typical p.e. curve you have seen before). The system depicted means we started with A and BC and ended with AB and C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to products not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier and regenerate the reactants.

For a given potential surface, The outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)). Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even if one has enough energy to surmount the barrier.

In the program you will use, you will run trajectories on several potential surfaces for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:30:19Z

Mjbear:

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

This exercise is designed to make you think about transition states, reaction coordinates and potential energy surfaces. You should discover that, for a chemical reaction to take place, having sufficient energy to overcome a barrier is not enough: the energy must also be in the right vibrational modes at the right time. You'll see trajectories cross the barrier, as if a reaction is going to take place, but then go back to reactants, with energy exchanged between translation and vibration.

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below, which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. (The form of the "F=ma" equation changes slightly as a result, but this is a detail that does not need to concern us.)

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms specified and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2 and m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be constant (but it may vary slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be constant (but it may vary slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a three dimensional '''potential energy surface''' where potential energy is plotted as a function of r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2 '''and the products ('''r1''' small '''r2''' large). (You may note that the variation of PE along the r2 and r1 axes is the typical p.e. curve you have seen before). The system depicted means we started with A and BC and ended with AB and C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to products not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier and regenerate the reactants.

For a given potential surface, The outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)). Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even if one has enough energy to surmount the barrier.

In the program you will use, you will run trajectories on several potential surfaces for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:23:58Z

Mjbear: /* The Write-up Required */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The write-up Required ===
A data sheet template/guide to the write-up and points for discussion required is available here (MAKE LINK).

Enter data and include screenshots in the data sheet at points indicated '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the concepts introduced.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy Surfaces (PESs)
* 27.8 Some results from experiments and calculations with PESs
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculating Molecular Dynamics trajectories.'''''

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (collision theory - Dr Oscar Ces)
* Spectroscopy, Quantum Chemistry (vibrational energy, harmonic oscillator - Prof Klug, Dr Wilde).
* Introduction to Physical Organic Chemistry (Transition states, activation enthalpies, reaction energy profiles (2D) - Prof McCulloch).

Having completed the exercise you will be better prepared to understand material in year 3 where the Molecular Reaction Dynamics course (Prof Yaliraki) in particular builds on the ideas and concepts developed here.

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual 2 dimensional potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. The form of the "F=ma" equation changes slightly but this is a detail that does not need to concern us.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2 and m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be constant (but it may vary slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be constant (but it may vary slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a three dimensional '''potential energy surface''' where potential energy is plotted as a function of r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2 '''and the products ('''r1''' small '''r2''' large). (You may note that the variation of PE along the r2 and r1 axes is the typical p.e. curve you have seen before). The system depicted means we started with A and BC and ended with AB and C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to products not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier and regenerate the reactants.

For a given potential surface, The outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)). Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even if one has enough energy to surmount the barrier.

In the program you will use, you will run trajectories on several potential surfaces for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:15:10Z

Mjbear: /* Obtaining the software */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== The software ==

Instructions on how to run the software and obtain the data files required for this experiment are here: [[Running MD code in MATLAB]].

== Introduction ==

=== The Write-up Required ===
A template/guide to the write-up required and points for discussion are included at the end of the exercise. A (proforma) data sheet is attached. You might find it convenient to enter data and make sketches, or include screenshots, in the data sheet at points indicated in the text by '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the more complex examples that you will tackle later in this exercise particularly in part 2.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy (P.E.) Surfaces
* 27.8 Some results from experiments and calculations with P.E.
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculations using Molecular Reaction Dynamics.'''''

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (Intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (Collision Theory – Kinetics - Dr Oscar Ces)
* Spectroscopy (Quantum Chemistry – vibrational energy, the vibrating molecule - Dr Klug, Dr Bearpark).
* Introduction to Physical Organic Chemistry (Transition states activation enthalpies and entropies, reaction energy profiles (2D) . Prof I McCulloch).

This exercise now adds an extra layer of subtlety to the basic information presented in year 1 – particularly with regard to making the model of simple reactions more sophisticated as noted on the previous page.

Having completed the exercise you will be better prepared to understand material in year 3 where the molecular reaction dynamics course in particular builds on the ideas and concepts used here.

This material will be explored and developed next year in the following courses:
* Statistical Thermodynamics
* Molecular Reaction Dynamics

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual 2 dimensional potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. The form of the "F=ma" equation changes slightly but this is a detail that does not need to concern us.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2 and m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be constant (but it may vary slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be constant (but it may vary slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a three dimensional '''potential energy surface''' where potential energy is plotted as a function of r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2 '''and the products ('''r1''' small '''r2''' large). (You may note that the variation of PE along the r2 and r1 axes is the typical p.e. curve you have seen before). The system depicted means we started with A and BC and ended with AB and C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to products not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier and regenerate the reactants.

For a given potential surface, The outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)). Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even if one has enough energy to surmount the barrier.

In the program you will use, you will run trajectories on several potential surfaces for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:13:32Z

Mjbear: /* Molecular Reaction Dynamics: Applications to Triatomic systems */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

''Based on a'' s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== Obtaining the software ==

Instructions on how to obtain and run the software required to run this experiment can be obtained in the page [[Running MD code in MATLAB]].

== Introduction ==

=== The Write-up Required ===
A template/guide to the write-up required and points for discussion are included at the end of the exercise. A (proforma) data sheet is attached. You might find it convenient to enter data and make sketches, or include screenshots, in the data sheet at points indicated in the text by '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the more complex examples that you will tackle later in this exercise particularly in part 2.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy (P.E.) Surfaces
* 27.8 Some results from experiments and calculations with P.E.
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculations using Molecular Reaction Dynamics.'''''

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (Intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (Collision Theory – Kinetics - Dr Oscar Ces)
* Spectroscopy (Quantum Chemistry – vibrational energy, the vibrating molecule - Dr Klug, Dr Bearpark).
* Introduction to Physical Organic Chemistry (Transition states activation enthalpies and entropies, reaction energy profiles (2D) . Prof I McCulloch).

This exercise now adds an extra layer of subtlety to the basic information presented in year 1 – particularly with regard to making the model of simple reactions more sophisticated as noted on the previous page.

Having completed the exercise you will be better prepared to understand material in year 3 where the molecular reaction dynamics course in particular builds on the ideas and concepts used here.

This material will be explored and developed next year in the following courses:
* Statistical Thermodynamics
* Molecular Reaction Dynamics

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual 2 dimensional potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. The form of the "F=ma" equation changes slightly but this is a detail that does not need to concern us.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2 and m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be constant (but it may vary slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be constant (but it may vary slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a three dimensional '''potential energy surface''' where potential energy is plotted as a function of r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2 '''and the products ('''r1''' small '''r2''' large). (You may note that the variation of PE along the r2 and r1 axes is the typical p.e. curve you have seen before). The system depicted means we started with A and BC and ended with AB and C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to products not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier and regenerate the reactants.

For a given potential surface, The outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)). Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even if one has enough energy to surmount the barrier.

In the program you will use, you will run trajectories on several potential surfaces for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

CP3MD

2016-04-20T11:13:05Z

Mjbear: /* Molecular Reaction Dynamics: Applications to Triatomic systems */

= Molecular Reaction Dynamics: Applications to Triatomic systems =

Based on a s''cript revised in Feb 2015 by Pietro Aronica and Paul Wilde.''

'''''Note: all distances and velocities are in atomic units for this exercise '''''

== Obtaining the software ==

Instructions on how to obtain and run the software required to run this experiment can be obtained in the page [[Running MD code in MATLAB]].

== Introduction ==

=== The Write-up Required ===
A template/guide to the write-up required and points for discussion are included at the end of the exercise. A (proforma) data sheet is attached. You might find it convenient to enter data and make sketches, or include screenshots, in the data sheet at points indicated in the text by '''==> data sheet'''

=== Background reading ===
Note that it is possible to start this exercise and run some trajectories very easily but reference to literature will be needed to understand the more complex examples that you will tackle later in this exercise particularly in part 2.

'''Atkins and de Paula:''' Physical Chemistry, 7th Edition. Topic titles are provided so that you can find the material in later editions of this textbook or in other textbooks.
* Chapter 25: The Rates of Chemical Reactions
* Section 25.5 - T dependence of reaction rates, Arrhenius Parameters their determination and interpretation.
* Chapter 27 Molecular Reaction Dynamics.
* Sections 27.4 Activated Complex Theory, The Eyring Equation.
* 27.5 Thermodynamic aspects of activated complex theory
* 27.6- Dynamics of Molecular Collisions.
* 27.7 Potential Energy (P.E.) Surfaces
* 27.8 Some results from experiments and calculations with P.E.
Note that many other physical chemistry textbooks will also cover this material. Editions of Atkins will vary in their coverage.

=== Objectives ===
'''''The objectives of this exercise are to study the reactivity of triatomic systems, where an atom and a diatomic molecule collide, through calculations using Molecular Reaction Dynamics.'''''

The gas phase collision and reaction between an atom and a linear diatomic molecule will be studied. If the reaction proceeds it will form a new diatomic molecule and atom. This exercise builds a level of sophistication upon previous kinetic treatments that you have seen by examining other types of energy (e.g. vibrational) that may be needed for reaction or present in products and also by illustrating how certain conditions lead to reaction profiles which simpler models do not predict.

=== Relevance to other courses ===

A lot of the background material for this exercise has been covered in courses you have taken in year 1.

* Molecular Driving Forces (Intermolecular interactions - Dr. Ian Gould)
* Chemical Kinetics (Collision Theory – Kinetics - Dr Oscar Ces)
* Spectroscopy (Quantum Chemistry – vibrational energy, the vibrating molecule - Dr Klug, Dr Bearpark).
* Introduction to Physical Organic Chemistry (Transition states activation enthalpies and entropies, reaction energy profiles (2D) . Prof I McCulloch).

This exercise now adds an extra layer of subtlety to the basic information presented in year 1 – particularly with regard to making the model of simple reactions more sophisticated as noted on the previous page.

Having completed the exercise you will be better prepared to understand material in year 3 where the molecular reaction dynamics course in particular builds on the ideas and concepts used here.

This material will be explored and developed next year in the following courses:
* Statistical Thermodynamics
* Molecular Reaction Dynamics

=== Theory ===

==== Introduction ====

We're able to simulate a reaction by treating the molecule and atom that are reacting as if they were “billiard balls colliding into each other”. They have masses, positions, accelerations and speeds and using these properties we can analyse how a reaction might proceed. Because nuclei are so much heavier than electrons, we can focus on the nuclei alone.

It is possible to understand much of chemical reactivity using classical Newtonian mechanics for the nuclei. This is because electrons move very rapidly (they have much lower mass) compared to the speed of nuclear motion. You have seen a number of occasions where the separation of nuclear and electronic motion has been used before (e.g. Born Oppenheimer Approximation and the Franck-Condon Principle). In Newton’s notation, a dot over a quantity indicates the first derivative and two dots the second derivative. If r represents position and V(r) potential energy then we have the equations below which are equivalents to the more familiar F= ma etc.

<math>m \ddot{r} = - { dV(r) \over dx}</math>

<math>\ddot{r} = \text{acceleration}</math>

<math>\text{Force} = - { dV(r) \over dx}</math>

'''m '''is a column vector that contains the masses of the nuclei, '''r''' is a position vector that contains the Cartesian co-ordinates of the atoms and '''V(r) '''is the potential energy function. (For a diatomic molecule '''V(r) '''is just the usual 2 dimensional potential energy curve that expresses the change in the energy as the two nuclei are displaced from their equilibrium positions by changing the interatomic distance – making the separation too small leads to a rapid rise in potential energy and increasing the bond length also leads to an increase in energy (and eventually to dissociation).

Molecular Dynamics ''simulation'' of the system involves solving these equations expressing the changes in the atomic co-ordinates etc. at a time increment ∆t:

<math>r_{i}(t + \Delta{t}) = r_{i}(t) + \Delta{t} \dot{r}_{i}(t + \Delta {t}) </math>

<math>\dot{r}_{i}(t + \Delta{t}) = \dot{r}_{i}(t) + \Delta{t} \ddot{r}_{i}(t + \Delta {t}) </math>

The time step (∆t) used is typically 0.1 fs (femtosecond = 10-15 sec). In this way one obtains a ''classical trajectory'' '''r(t)''' that describes how the system evolves in time. The trajectory represents a path across the potential energy surface (you will see examples shortly). Such simulations have many applications in chemistry and biology and you may well encounter these in higher level lecture courses in year 4. In the computations you will perform, it is convenient to use internal coordinates (bond lengths and angles) rather than Cartesian coordinates of the atoms. The form of the "F=ma" equation changes slightly but this is a detail that does not need to concern us.

'''Note that the program does all these calculations for you. You input bond distances and momenta for the atoms and the potential energy surface and the trajectory the system follows across the surface is calculated for you. Your job is to interpret the results.'''

==== Atom-Diatom Collisions ====
In this exercise we will apply this method to study atom diatom collisions. A typical example is depicted below.

[[File:Y2C1.png|thumb|left|400px|'''Figure 1: ''An example of a triatomic exchange reaction''''']]
 

In simple terms, the atom m1 collides with the molecule and forms a new molecule with m2 and m3 is detached as a separate atom.

If we think about how the distances r1 and r2 change during this process we can make several deductions.

Before the collision/reaction:
* r2 will be constant (but it may vary slightly if the molecule has vibrational energy).
* r1 is decreasing steadily as m1 gets closer to m2.

After the collision/reaction:
* r1 will now be constant (but it may vary slightly if the molecule has vibrational energy).
* r2 is increasing steadily as m3 moves away from the molecule formed from m2 and m1.

This means that instead of our simple picture of energy versus reaction coordinate we can map the progress of this reaction on a three dimensional '''potential energy surface''' where potential energy is plotted as a function of r1 and r2. We thus obtain a '''''contour plot''''' like the one shown in '''Figure 2'''. For a linear triatomic exchange reaction, the potential function '''V''' is a function of only two parameters '''r1''' and '''r2'''. Thus we can plot the potential energy as a '''contour plot''' of '''V'''('''r1''','''r2''') versus '''r1''' and '''r2'''. A '''trajectory''' {'''r1'''(t) '''r2'''(t)} can then be drawn on this potential energy surface.

[[File:Y2C2.png|thumb|800px|left|'''Figure 2: ''An example of a reactive trajectory for H + H2 potential surface''''']]
 

In '''Figure 2''', the small boxes indicate the reactants ('''r1''' large '''r2''' small), a transition structure where '''r1'''='''r2 '''and the products ('''r1''' small '''r2''' large). (You may note that the variation of PE along the r2 and r1 axes is the typical p.e. curve you have seen before). The system depicted means we started with A and BC and ended with AB and C. A '''''reactive'' trajectory '''(it’s reactive because it proceeds all the way from reactants to products not all trajectories will do this) that passes through the '''''transition structure''''' is shown as a wavy line. (The transition structure is a saddle point in the potential energy surface). Notice that the trajectory shown involves vibration in '''r2''' (the molecule BC has vibrational energy) as the inter-fragment distance '''r1''' is ''decreased ''in the ''entrance ''channel (at the top left of the figure) and vibration in '''r1''' (the product AB has vibrational energy) as the inter-fragment distance '''r2''' is ''increased'' in the ''exit ''channel (at the right of the figure). An '''unreactive trajectory''' would bounce off the barrier and regenerate the reactants.

For a given potential surface, The outcome of a dynamics simulation (i.e. the positions '''r1'''(t), '''r2'''(t) and the momenta '''p1'''(t),''' p2'''(t)''' , pi '''=m'''vi''') at some time t are determined by the initial conditions at time t=0 (i.e. '''r1'''(0), '''r2'''(0) and the momenta '''p1'''(0),''' p2'''(0)). Only certain initial conditions will lead to a trajectory that passes via the transition structure to the products even if one has enough energy to surmount the barrier.

In the program you will use, you will run trajectories on several potential surfaces for a variety of input conditions. You will be able to ''animate'' the trajectory on the potential surface and examine the distribution of vibrational and translational energy in the products.

As a demonstration you will study the potential surface for an atom of H colliding with a molecule of hydrogen to illustrate the principles and to learn how to use the main features of the program. You will then experiment with some more subtle examples.

== EXERCISE 1: H + H2 system ==
The instructions for this exercise are rather verbose. The objective is to illustrate the various features of the program and then apply them to studying some aspects of this reaction which you report upon.

The first stages of this exercise are designed to familiarise you with the programme. They do not form part of the assessed work.

=== Viewing the potential surface ===

Before you begin experimenting with the different types of collision, note that the script makes reference to r1 and r2 whereas in the GUI the atoms are labelled A B and C and the distances are rAB and rBC. Since you run some trajectories in forward and reverse directions it is hard to develop a consistent notation. Thus before you run a trajectory, check carefully what you have set up. Your initial molecule will be defined by which of AB distance or BC distance you have set to be the bond distance. One distance will be short (the bond distance) and one will be long.

=== Run a reactive trajectory ===

In this part you are given a set of conditions such that the reaction depicted below will proceed. The example takes you through how to use the different options available (the different types of plot) to see what is happening for a particular reaction. Thus you explore the trajectory by looking at contour (2D) and surface (3D) plots and how internuclear distances, potential and kinetic energy and momenta change during the reaction.

The default settings of the positions and momenta are initialised to produce a ''reactive trajectory ''(like the one in Figure 2). In other words, these conditions should lead to the reaction below taking place. As you will see in later sections, not all trajectories you run will be reactive.

[[File:Y2C5.png|thumb|500px|left|'''Figure 3: ''Initial conditions that lead to reaction''''']]
 

The file you downloaded (lepsgui.m) has a set of initial conditions and will run with those when you first use the command and should show you a contour plot.

'''''To run the example above, first check the initial conditions you have in the GUI'''''. '''''If the initial conditions you have are not as noted above, then change as needed. '''''

For example in Figure 3 you can see both momenta are -2.7 so if you have rBC set at 0.74 make sure BC momentum is changed to 0.0.

* Check the initial conditions that are shown in the menu are as follows: ('''r1'''(0) = 0.74 '''r2'''(0) = 2.30 and the momenta '''p1'''(0)=0 ''' p2'''(0) = -2.7).
* A ''negative ''value of the momentum corresponds to a velocity that ''decreases'' the interatomic distance. Thus in this case we are starting the trajectory by giving the system some velocity in the direction that decreases '''r2''' (refer to the diagram above).

You can see from a comparison of this data with Figure 3 that in this case BC is the molecule with a bond distance = 0.74 and A is the atom that collides with it. Thus here r1 = rBC.

* The program updates the image on the right whenever you press the “Update” button at the top (see Figure 4 below). When you started the program, it will have automatically calculated the trajectory with the initial conditions outlined above and shown you the contour plot. To see other plots, such as plots of velocities and positions against time, or a 3D surface plot of the reaction, select that option from the drop down menu at the bottom left and press update. You can have a better look at the surface plot by rotating it (the button on the bar at the top with the arrow circling the cube). Spend some time to have a look at the various options.
* Figure 4 shows some of the controls and how they can be used.

[[File:Y2C6.png|thumb|500px|left|'''Figure 4: ''The key controls and icons that you will use''''']]
 

* Select “'''Surface Plot'''”, which gives you a plot of the Potential Energy Surface (PES). The thick black line in the middle is the path of the reaction. Try to identify the reactants’ and products’ channels. Observe how the line is wavy: this represents the vibrational nature of the system. The most important point to observe is conservation of energy: '''''the system will always oscillate between energy contours with the same value'''.''
* To animate the geometry, select the last option, “'''Animation'''”, in the drop down menu at the bottom left. You will see that initially r2 decreases as H3 approaches H1-H2, then after the transition state, H1 leaves and H2-H3 is formed in a vibrationally excited state.
* This same information can be displayed in a different form by selecting “'''Internuclear Distances vs Time'''” in the same menu. In this graphical display the values of r1(t), r2(t) are given (Y axis ) against time t (X axis). Notice that r2 (rAB here) decreases from the original value of 2.3 during the first 0.38 time units, then it has an oscillatory behaviour for the remainder of the trajectory corresponding to H2-H3 vibration. In contrast r1 (rBC here) has a slight oscillatory behaviour initially, then after the transition state, it grows in value as H1 leaves. Notice that r1(t) = r2(t) at ≈ 0.38 s. This is effectively the transition state.

[[File:Y2C7.png|thumb|500px|left|'''Figure 5: ''r1(t) and r2(t) are given (Y axis ) against time t (X axis). Note that only two distances are shown on this plot. The GUI shows three.''''']]
 

* Next, select “'''Potential Energy vs Time'''” in the same menu. It will show an oscillatory behaviour rising in energy until the transition state is reached. The potential energy then falls as the trajectory moves into the exit channel. The energy is continually switching from potential energy to kinetic energy during the trajectory. At the turning point of a trajectory one is at the maxima of the oscillations. At the bottom of the trough of the oscillations the potential energy is low and the molecule is moving faster so the energy has gone into kinetic energy. You can see this with “'''Kinetic Energy vs Time'''”. In this case the kinetic energy reaches its ''minimum'' value at the transition state (i.e. the system is moving slowly)
* Finally the momenta '''p1'''(t) and''' p2'''(t)''' '''('''pi '''=m'''vi'''), can be displayed using “'''Internuclear Momenta vs Time'''”. This result is not easy to interpret because the momenta correspond to bond stretching displacements '''r1 '''and '''r2 '''as illustrated below.

[[File:Y2C8.png|thumb|500px|left|'''Figure 6: ''Momenta p1 and p2 correspond to those that change the interatomic distances, not the atoms themselves''''']]
 

Thus '''p1''' is the momentum in the coordinate '''r1'''. Notice that the momentum in the atom 2 results from both momenta '''p1''' and '''p2'''. Thus if we want to collide atom 3 with 1-2 (by giving some '''p2''') in such a way that the diatom 1-2 does not vibrate, we must give some momentum in '''p1''' as well. Following the momentum distribution from the transition state provides some insight as we now discuss.

The important observations are as follows:

Initially '''p1'''(0)=0 and '''p2'''(0)=-2.7. At the beginning of the trajectory '''p2'''(t) decreases and '''p1'''(t) takes on an oscillatory behaviour. '''p1'''(t) oscillates because the initial momentum in '''p2''' also forces '''r1''' to change as is evident from the picture above. After the transition state at t=0.38, '''p1'''(t) rises rapidly and remains constant (corresponding to translation) as '''r1''' becomes large as H1 leaves. In contrast '''p2 '''initially corresponds to translation. After the transition state '''p2''' oscillates (corresponding to vibration).

=== Dynamics from the transition state region ===

[[File:Y2C9.png|thumb|600px|left|'''Figure 7: ''Gradients at the TS region''''']]
 

The '''''transition state''''' is defined as a '''''high point''' ''on the '''''lowest energy path''''' between the reactants and the products. It has the special property that at this point dV('''r''')/d'''r''' is zero. Consequently, if one starts a trajectory exactly at the transition state with no initial momentum it will remain there forever. If one changes the geometry by a small amount in the direction of the products it will roll towards the products (and similarly for the reactants). One way of locating the transition state is to start trajectories near the transition state and see whether they "roll" towards the reactants or products. The ''reaction path'' (minimum energy path or '''mep''') is a very special trajectory that corresponds to infinitely slow motion (i.e. the velocity always zero). Once the transition state has been located one may run the very special trajectory that corresponds to the '''mep'''.

Since the H + H2 surface is symmetric, the transition state must have '''r1''' = '''r2'''. If we start a trajectory on the ridge '''r1''' = '''r2 '''there is no gradient in the direction at right angles to the ridge, thus the trajectory will oscillate on the ridge and never fall off. As we will see, this fact can be used to locate the TS geometry. If we start a trajectory at '''r1''' = '''rts+'''δ and '''r2''' = '''rts''' the trajectory “falls off” the '''r1''' = '''r2 '''ridge. We begin by running trajectories from near the TS geometry.

'''''REMOVE(?) To this point, you have been learning how to use the program to visualise a reaction. From now on you will be exploring the factors that influence whether or not a trajectory is reactive and why. You should make a note of the key data and results because they should be included in your report. From this point on the work you do should be included in your report and will be assessed.'''''

==== Trajectories from r1 = r2: locating the transition state ====
* Use the menus and buttons on the left of the GUI to modify the initial conditions.
* First set the momenta to exactly 0. Type in values of the momenta corresponding to '''p1''', '''p2. You should supply exactly 0.0 here.'''
* Then type in values of '''r1''', '''r2. '''You should supply one choice of values of''' r1''' and '''r2''' that are exactly equal in the region of 0.85 to 0.95. To see the reaction path, select “'''Contour'''” or “'''Surface Plot'''” on the bottom menu, then press “'''Update'''” to visualise. If you select “'''Animation'''”, you will see that the system undergoes a periodic symmetric vibration of the form shown in '''Figure 8'''.

[[File:Y2C10.png|thumb|500px|left|'''Figure 8: ''Symmetric vibration about the TS''''']]
 

* Now select “'''Internuclear Distances vs Time'''”. You will see that the plots for '''r1 '''and '''r2 '''are superimposed because they are oscillating exactly in phase. You will thus only be able to see two of the three colours on this example. The geometry about which they are oscillating is the transition state geometry. Determine this value of''' r1''' = '''r2''' as accurately as you can from the graph. As further proof that you have found the value, try typing it in the initial conditions: it should give you a straight line without oscillation. We shall refer to this value as '''rts'''. '''''Make a note of this value.'''''

==== Trajectories from r1 = rts+δ, r2 = rts ====
* Now we will run trajectories in the '''forward''' and '''reverse''' directions from '''r1''' = '''r2''' = '''rts '''with '''p1''' = '''p2''' = 0. This can be accomplished by running trajectories with '''r1''' = '''rts''' and '''r2''' = '''rts+0.01'''. This should terminate at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3'''. You might convince yourself that a trajectory with '''r1''' = '''rts+0.01''' and '''r2''' = '''rts''' will give similar results terminating at '''r1''' > 2.0 with '''r2''' oscillating i.e. at '''H1+ H2'''-'''H3'''.
Use different plots ('''Contour, Surface, Animation''') to analyse the system.
* Finally, look at “'''Internuclear Distances vs Time'''” and note the final values of the positions '''r1'''(t) '''r2'''(t) and the average momenta '''p1'''(t)''' p2'''(t) (using “'''Internuclear Momenta vs Time'''” at large t for later use.
'''''Write these down on the data sheet.'''''

Consider the results of the trajectory with '''r1''' = '''rts''' and '''r2''' = '''rts'''+0.01 which terminated at '''r2''' > 2.0 with '''r1''' oscillating i.e. at '''H1-H2 '''+ '''H3''' Thus asymptotically, the '''r1''' oscillates about the '''H1-H2''' equilibrium bond length (0.74) as '''r2''' became large. The momentum '''p1 '''oscillates around 1.25''' '''(i.e. between .8 and 1.5)''' '''while '''p2''' becomes constant at around 2.5. By simply reversing the signs of the final momenta we can run the trajectory backwards to give a reactive trajectory. This data tells us that any trajectory will be reactive for '''r1''' = 0.74, '''r2''' = 2.0, with''' '''-'''1.0 < p1 < '''-'''1.5 '''and''' p2''' = -2.5

==== The mep from r1 = r2 ====
Next, we will look at the '''mep.''' Leave the geometry and momenta as in the previous exercise (i.e. the positions '''r1''' = '''rts'''+.01, '''r2''' = '''rts''' and the momenta '''p1'''=0 and''' p2'''=0), then change the calculation type from dynamics to MEP. You will see that the trajectory simply follows the valley floor to '''H1+ H2'''-'''H3'''

=== Generating reactive trajectories ===
How do we determine the conditions for a reactive trajectory that starts in the region of the reactants and passes near the TS region? As you will discover, simply adjusting the collision parameters so that the system has enough energy to reach the '''TS''' is not enough. ''The energy must be distributed correctly. ''
* Change the computation type back to Dynamics.

* From our computations that began at the transition state with '''r1''' = '''rts''' and '''r2''' = '''rts'''+ 0.01 we know that a reactive trajectory will correspond to '''r1''' = '''0.74''', '''r2''' = '''2.0''', with''' -0.8 < p1 < -1.5''' and''' p2 '''=''' -2.5'''
* Run several trajectories with fixed values of '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p2 '''=''' -2.5''' but with''' -0.8 < p1 < -1.5. ''' They should all be reactive. Note that '''p1 is varied here. Make sure your conditions are correct before you start.'' Report on the data sheet conditions that you used and the characteristics of the trajectories that you observe.'''''

* Run the trajectory with '''r1''' = '''0.74''' '''r2''' = '''2.0''', '''p1 '''= '''-1.25 '''and '''p2 '''=''' -2.5'''. '''''What do you note about the behaviour in the entrance channel? Report on the data sheet.'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1''' = '''-1.5''', '''p2 '''=''' -2.0'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why?'''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''1.5''',''' p2 '''=''' -2.5'''. '''''Report on the data sheet. Is the trajectory reactive or unreactive? Why? '''''

* Run a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1'''= '''-2.5''', '''p2 '''=''' -5.0''' (i.e. similar to the trajectory where we force pure translation in the input channel but with the momenta twice as large). The result is quite remarkable: The trajectory actually crosses the transition state region but does not go on to products even though we have given it more than twice the momentum needed to surmount the barrier. It is instructive to use “'''Animation” '''for this example. You should see the bond in the product actually forms but then the system reverts back to the reactants. '''''Report on the data sheet.'''''

[[File:Y2C11.png|thumb|600px|left|'''Figure 9: ''Trajectory that re-crosses the TS region''''']]
 

* Running a trajectory with '''r1''' = '''0.74''', '''r2''' = '''2.0''', '''p1 '''= '''-2.5''', '''p2 '''=''' -5.2 '''produces an unusual result. '''''Report on the data sheet.'''''

'''Discussion''': In the transition state theory of reaction rates it is assumed once the system reaches the transition structure it goes on to produce products. However transition state theory usually overestimates the reaction rate. Why?

=== Guidance on your report for Part 1 the H and H2 system ===
Summarise in less than 200 words the main aims and objectives of this first part of the experiment including in your brief outline how chemical reactivity can be studied using classical trajectories computed from the gradient on the potential energy surface.

Reading the discussions in Atkins (references in the script are to the 7th edition but the topics discussed can be found in earlier and later editions and in many more textbooks) and the handout itself should help to complete this short introduction.

==== Discussion of the first part of the exercise ====
The reaction between H and H2 has been studied here. Use the data sheet and the observations that you recorded there to structure your results and discussion. You can either expand on the data sheet by including a short introduction (as indicated above) and then the data with suitable results (screenshots) to illustrate the outcome of each trajectory and the reasons why a particular outcome is observed for a particular set of conditions. You may also, if you wish, write the report separately.

Your focus should be to report the outcomes of the trajectories that you have run, whether they are reactive or unreactive and any key observations that particular trajectories show.

== EXERCISE 2: F + H2 system ==
* Select the F + H2 potential surface by changing the atom types in the GUI. View the surface plot (potential surface). You need not worry about the conditions as the point is to view the surface, not a trajectory.
* You will see that the reaction is highly exothermic (i.e. the exit channel is much lower in energy than the entrance channel since the HF bond is much stronger than the HH bond). Furthermore, there appears to be no transition state.
* Because the entrance and exit channels are so different, you may need to experiment with the 3D view rotation (see instructions for part 1) to find the most informative point of view.

The '''mep''' has the following form:

Close inspection shows that there is a barrier in the entrance channel (and consequently a transition state) but the barrier height is so small that it is not within the resolution of the program you are using. At the transition state '''r1''' (F-H2) = '''1.33 '''and '''r2 '''(FH-H) = '''0.85'''. Because the reaction is exothermic, the transition state is reactant-like and occurs in the entrance channel (an ''early barrier'').

(This isn't the TS for me. I'm getting r1=1.85 and r2=0.75 [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 17:12, 19 April 2016 (BST))

With an exothermic reaction such as this one you may find it useful to explore the potential energy surface and the trajectories using the data cursor. Figure 10 below shows the icon on the toolbar. Clicking on the icon allows you to interrogate part of the surface to find coordinates and energy values (indicated by level – see the Figure).

[[File:Y2C12.png|thumb|600px|left|'''Figure 10: ''The data cursor allows you to map the surface and find coordinates (rAB, rBC and energy (“level”).)''''']]
 

=== Run an mep computation from the TS r1 = 1.33 and r2 = .85 ===
Set the distances and momenta to '''r1''' = '''1.33''',''' r2''' = '''0.85''', '''p1 '''= '''0''' and''' p2 '''= '''0'''. Then '''select the calculation type MEP''' and run the trajectory in the usual way. You will see that the trajectory simply follows the valley floor to '''F-H '''+''' H. '''

'''''Include a brief discussion and illustration of the mep in your report.'''''

=== Dynamics computation from the TS: Release of the energy of exothermicity ===
* Change the calculation type back to Dynamics.
* Run the trajectory again. Examine the results with “'''Animation”''', and look at the “'''Internuclear Distances vs Time'''” and “'''Internuclear Momenta vs Time”.'''
* What do you conclude about the release of the exothermicity of the reaction into translational and vibrational energy?

'''''Include a brief discussion of the energy release for this exothermic reaction with suitable illustrations in your report.'''''

Mod:phys3

2015-12-18T11:11:42Z

Mjbear: /* Discussion */

See also: [[Mod:intro|General info]],  [[mod:programs|Programs]],  [http://www.gaussian.com/g_tech/gv5ref/gv5ref_toc.htm Gaussian Online User Manual] | [http://faculty.ycp.edu/~jforesma/educ/visual/index.html Visualization Tutorials]
= Module 3 =

In this set of computational experiments, you will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

There are two parts:

a) tutorial material: how to use the programs and methods,

b) more challenging examples, with guidelines but fewer explicit instructions.



''As a guideline, you should aim to complete part (a) in the first week of the experiment. Do not rush the tutorial material: once you have a good understanding of the computational techniques and how to work with the codes, you will find the remaining parts more straightforward and be better able to solve any problems you encounter. Try to write up sections on your wiki in outline as you go. Include the tutorial material in your write-up. If you are having problems, talk them through with a demonstrator or staff at the first opportunity.''

In the second year physical chemistry laboratory, you may have carried out dynamics calculations using model potential energy surfaces to explore transition states. In that computational experiment, the total energy could quickly be calculated for different geometries of a triatomic system using an analytical function of the atomic coordinates (for more information, see for example [http://books.google.com/books?id=T8IZ1aa_FRkC&pg=RA1-PA36&lpg=RA1-PA36&dq=%22lake+eyring%22&source=web&ots=OXY00lSZ7D&sig=Ld_MTNwNjUDNGzB_5w1IxaMBMPU&hl=en&sa=X&oi=book_result&resnum=7&ct=result here] and [http://www.rsc.org/ejarchive/DC/1979/DC9796700007.pdf here]).

In this experiment, you will be studying transition structures in larger molecules. There are no longer fitted formulae for the energy, and the molecular mechanics / force field methods that work well for structure determination cannot be used (in general) as they do not describe bonds being made and broken, and changes in bonding type / electron distribution. Instead, we use molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface. As well as showing what transition structures look like, reaction paths and barrier heights can also be calculated.

Information that you might find useful in your wiki writeup is giving in the [[Mod:Cheatsheet|cheatsheet]].

==The Cope Rearrangement Tutorial==



''This part of the module is described as a 'tutorial' because it's an introduction to various computational techniques for locating transition structures on potential energy surfaces. It's different to the [[mod:gv_basic |GaussView Tutorial]] you can work through: it's an exercise where you're given specific instructions, then see if you can follow them, and also determine whether there are problems or better ways of carrying the exercise out. Please include this part in your write-up. Marks will be given for correct answers, the documentation showing how you got these, discussion, and how you went about solving any problems you encountered.''

In this tutorial we will use the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem.

Your objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

This [3,3]-sigmatropic shift rearrangement has been the subject of numerous experimental and computational studies (e.g. Houk et al. {{DOI|10.1021/ja00101a078}}), and for a long time its mechanism (concerted, stepwise or dissociative) was the subject of some controversy. Nowadays it is generally accepted that the reaction occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy. The B3LYP/6-31G* level of theory has been shown to give activation energies and enthalpies in remarkably good agreement with experiment. In this tutorial we will show how these can be calculated using Gaussian.

 

{| align="center"
|- align="center"
|
[[Image:pic2a.jpg]]
|
[[Image:pic2b.jpg]]
|- align="center"
| align="center" | ''Chair Transition State''
| align="center" | ''Boat Transition State''
|}

 

===Optimizing the Reactants and Products===

'' In this section you will learn how to optimize a structure, symmetrize it to find its point group, calculate and visualize vibrational frequencies and correct potential energies in order to compare them with experimental values. It is assumed that you are already familiar with using the builder in GaussView. ''

 

(a) Using GaussView, draw a molecule of 1,5-hexadiene with an "anti" linkage (approximately a.p.p conformation) for the central four C atoms . Clean the structure using the '''Clean''' function under the '''Edit''' menu.

Now we will optimize the structure at the '''HF/3-21G''' level of theory. Select '''Gaussian''' under the '''Calculate''' menu, click on the '''Job Type''' tab and choose '''Optimization'''. The default method should already be Hartree Fock and the default basis set is 3-21G, so there should be no need to change these. You can check this by clicking on the '''Method''' tab. Submit the job by clicking on the '''Submit''' button at the bottom of the window and give the job a meaningful name (e.g. react_anti).

When the job has finished, you will be asked if you want to open a file. Select '''Yes''' and choose the checkpoint (chk) file with the name of the job you have just run (e.g. react_anti.chk). This checkpoint file is a binary file that stores data calculated by Gaussian. The name of the chk file should have been assigned by default. Once the file has been opened, click on the '''Summary''' button under the '''Results''' menu and make a note of the energy.


Does your final structure have symmetry? Select '''Symmetrize''' under the '''Edit''' menu (note that sometimes it is necessary to relax the search criteria under the '''Point Group''' menu). Make a note of the point group.

'''Warning:''' Clicking '''Symmetrize''' will change the geometry of your structure and cause a lot of the data to be discarded (including the energy data in the summary window). Instead, simply make a note of the point group that appears in the centre left of the '''Point Group Symmetry''' window. If it doesn't appear, incrementally relax the tolerance (centre of window) until it does. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 16:27, 14 October 2015 (BST)

 

(b) Now draw another molecule of 1,5-hexadiene with a "gauche" linkage for the central four C atoms. Would you expect this structure to have a lower or a higher energy than the anti structure you have just optimized? Optimize the structure at the '''HF/3-21G''' level of theory and compare your final energy with that obtained in (a). Again, check if the molecule has symmetry and make a note of the point group.

 

(c) Normally, calculated activation energies and enthalpies use the lowest energy conformation of a reactant molecule as a reference. What would you have expected the lowest energy conformer of 1,5-hexadiene to be? Explain your reasoning, draw this structure and optimize it (if you have not already). A table containing the low energy conformers of 1,5-hexadiene and their point groups is shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Draw gauche3 from the appendix and optimize it (again, if you have not already) and explain why this is the lowest conformer.

 

(d) Compare the structures that you have optimized in a) and b) with those in the table and see if you can identify your structure.

 

(e) Draw the Ci ''anti2'' conformation of 1,5-hexadiene (unless you have already located it). Optimize it at the '''HF/3-21G''' level of theory and make sure it has Ci symmetry. Compare your final energy to the one given in the table.


 

(f) When you are happy that your structure is the same as the one in the table, reoptimize it at the '''B3LYP/6-31G*''' level (6-31G* is equivalent to 6-31G(d) by selecting '''DFT''' under the '''Method''' menu and '''B3LYP''' from the box with the functionals on the right-hand side. Now select '''Link 0''' and change the name of the chk file to the name of the DFT optimization that you are about to run. Note that it is always advisable to do this when re-using or modifying existing structures to ensure that the original chk file is not overwritten. Run the job and make a note of the energy. Now compare the final structures from the '''HF/3-21G''' calculation with that at the higher level of theory. How much does the overall geometry change?

'''Note:''' It is meaningless to compare the energy of different levels of theory. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 16:10, 14 October 2015 (BST)

 

(g) The final energies given in the output file represent the energy of the molecule on the bare potential energy surface. To be able to compare these energies with experimentally measured quantities, they need to include some additional terms, which requires a frequency calculation to be carried out. The frequency calculation can also be used to characterize the critical point, i.e. to confirm that it is a minimum in this case: that all vibrational frequencies are real and positive.

Starting from your optimized B3LYP/6-31G* structure, run a frequency calculation at the same level of theory. You can do this by selecting '''Frequency''' under the '''Job Type''' tab. Ensure that the method is still correctly specified under the '''Method''' tab (''caution: on Windows, sometimes 'scrf=(solvent=water,check)' is incorrectly added!'') and then change the name of the chk file under the '''Link 0''' tab to the name of the frequency job that you are about to run. Run the job. Once the job has finished, open the log file this time. Select '''Vibrations''' under the '''Results''' menu. A list of all the vibrational frequencies modes should appear. Check that there are no imaginary frequencies, only real ones. You can visualize some of these vibrations under this menu and simulate the infrared spectrum.


Now, select '''View File''' under the '''Results''' menu and open the output file in the visualizer. Scroll down to the section beginning '''Thermochemistry'''. Under the vibrational temperatures a list of energies should be printed. Make a note of (i) the sum of electronic and zero-point energies, (ii) the sum of electronic and thermal energies, (iii) the sum of electronic and thermal enthalpies, and (iv) the sum of electronic and thermal free energies. The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS). It is important to make sure that you select the correct energy/enthalpy term to compare to your experimental values. Note that these corrections can also be calculated at other temperatures using the '''Temperature''' option in Gaussian, If you have time, try to re-calculate these quantities at 0 K as shown in the [[mod:gv_advanced | Advanced GaussView Tutorial]].

 

===Optimizing the "Chair" and "Boat" Transition Structures ===

'' In this section you will learn how to set up a transition structure optimization (i) by computing the force constants at the beginning of the calculation, (ii) using the redundant coordinate editor, and (iii) using QST2. You will also visualize the reaction coordinate and run the IRC (Intrinisic Reaction Coordinate) and calculate the activation energies for the Cope rearrangement via the "chair" and "boat" transition structures. ''

 

The "chair" and "boat" transition structures for the Cope rearrangement are shown in [[Mod:phys3#Appendix 2|Appendix 2]]. Both consist of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

 

(a) Draw an allyl fragment (CH2CHCH2) and optimize it using the '''HF/3-21G''' level of theory. Your structure should look like one half of the transition structures shown below.

Now open a new GaussView window by going to the '''File''' menu and selecting '''New''' and then '''Create MolGroup'''. Copy the optimized allyl structure from the first calculation by selecting '''Copy''' under the '''Edit''' menu, and then paste it twice into the new window by selecting '''Paste''' and then '''Append Molecule'''. Now orient the two fragments so that they look roughly like the chair transition state below by using the '''Shift Alt keys + Left Mouse button''' to translate one fragment with respect to the other and the '''Alt key + Left Mouse button''' to rotate it. The distance between the terminal ends of the allyl fragments should be approximately 2.2 Å apart. Save this structure to a Gaussian input file with a meaningful name (e.g. chair_ts_guess).

'''Note:''' If you're having trouble getting the bond lengths close enough to each other, an exact match can be achieved with '''Symmetrize'''. Get as close as you can to the structure, then open the '''Point Group''' window in the '''Edit''' menu. Relax the tolerance until the appropriate symmetry is displayed on the left and click '''Symmetrize'''. You should now be able to match the bond lengths. [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 16:37, 14 October 2015 (BST)

We are now going to optimize this transition state manually in two different ways. Transition state optimizations are more difficult than minimizations because the calculation needs to know where the negative direction of curvature (i.e. the reaction coordinate) is. If you have a reasonable guess for your transition structure geometry, then normally the easiest way to produce this information is to compute the force constant matrix (also known as the Hessian) in the first step of the optimization which will then be updated as the optimization proceeds. This is what we will try to do in the next section. However, if the guess structure for the transition structure is far from the exact structure, then this approach may not work as the curvature of the surface may be significantly different at points far removed from the transition structure. In some cases, a better transition structure can be generated by freezing the reaction coordinate (using '''Opt=ModRedundant''' and minimizing the rest of the molecule. Once the molecule is fully relaxed, the reaction coordinate can then be unfrozen and the transition state optimization is started again. One advantage of doing this, is that it may not be necessary to compute the whole Hessian once this has been done, and just differentiating along the reaction coordinate might give a good enough guess for the initial force constant matrix. This can save a considerable amount of time in cases where the force constant calculation is expensive.

 

(b) Use Hartree Fock and the default basis set 3-21G for parts (b) to (f).

Create a new MolGroup ('''File → New → Create MolGroup''') and copy and paste your guess structure into the window. Now set up a Gaussian optimization for a transition state. Go to the '''Gaussian''' menu under '''Calculate''' and click on the '''Job Type''' tab. Select '''Opt+Freq''' and then change '''Optimization to a Minimum''' to '''Optimization to a TS (Berny)'''. Choose to calculate the force constants '''Once''' and in the Additional keyword box at the bottom, type '''Opt=NoEigen'''. The latter stops the calculation crashing if more than one imaginary frequency is detected during the optimization which can often happen if the guess transition structure is not good enough. Submit the job. If the job completes successfully, you should have optimized to the structure shown in [[Mod:phys3#Appendix 2|Appendix 2]] and the frequency calculation should give an imaginary frequency of magnitude 818 cm-1. Animate the vibration and ensure that it is the one corresponding to the Cope rearrangement.

When performing an optimisation and subsequent frequency calculation, the geometry is at a minimum energy when all the vibrational frequencies are positive. When checking for a TS, there must be only one imaginary frequency. Explain briefly in simple terms, what does this imaginary frequency represent, and where does it come from?
Hint: think of the role of the force constant in a one dimensional quantum harmonic oscillator, covered in the QM3 course

 

(c) Now we will try optimizing the transition structure again using the frozen coordinate method. Create a new MolGroup ('''File → New → Create MolGroup''') and copy and paste your guess structure into the window again. Now select '''Redundant Coord Editor''' from the '''Edit''' menu. Click on the highlighted file icon at the top left-hand corner (Create a New Coordinate) and a line should appear below saying '''Add Unidentified (?, ?, ?, ?)'''. Now go back to the GaussView window and select two of the terminal carbons from the allyl fragments which form/break a bond during the rearrangement. Return to the coordinate editor and select '''Bond''' instead of '''Unidentified''' and select '''Freeze Coordinate''' instead of '''Add'''. Now click on the icon again to generate another coordinate. This time select the opposite two terminal atoms and again select '''Bond''' and '''Freeze Coordinate'''. Click OK. Now set up the optimization as if it were a minimum and you should see the option '''Opt=ModRedundant''' already included in the input line. Submit the job.

'''Note:''' GaussView allows you to produce an input file with the frozen coordinate specified as e.g. <tt>B 5 1 2.200000 F</tt>. Unfortunately, a recent update to the Gaussian program means it does not recognise this syntax, and just ignores this line. This means that the coordinate ends up being optimised rather than frozen. Therefore do not use this method, but ensure the guess structure has suitable guess transition bond distances(~2.2 Å) using the ''Modify Bond'' tool in GaussView --[[User:Rzepa|Rzepa]] 14:39, 29 October 2012 (UTC)

'''Note 2:''' If you set the coordinate distance (i.e. B 5 1 2.2 B) and freeze it (i.e. B 5 1 F) as separate inputs to the modredundant editor, it appears to work as expected. (Lee)

'''Note 3:''' If you are having trouble with this section (bonds not freezing) open your input file in Notepad or Notepad++ and go to the bottom of the file. You will see the lines that you would expect to freeze the bonds there. Make sure the line matches the notation in Note 2 (B 5 1 F, for example will freeze the bond between atoms 5 and 1). [[User:Tam10|Tam10]] ([[User talk:Tam10|talk]]) 16:09, 14 October 2015 (BST)

 

(d) When the job has finished, open the chk file. You should find that the optimized structure looks a lot like the transition you optimized in section (b), except the bond forming/breaking distances are fixed to 2.2 Å. Now we are going to optimize them too. Open the '''Redundant Coord Editor''' from the '''Edit''' menu again and create a new coordinate as before by clicking on the icon, Select one of the bonds that was previously frozen and this time choose '''Bond''' instead of '''Unidentified''' and '''Derivative''' instead of '''Add'''. Repeat the procedure for the other bond. This time you need to set up a transition state optimization but we are not going to calculate the force constants as we did in section (b) (so we leave this option as '''Never'''), instead we will use a normal guess Hessian modified to include the information about the two coordinates we are differentiating along. Change the name of the chk file in '''Link 0''' if you do not want to write over the previous calculation and submit the job. When the calculation has finished, open the chk file, check the bond forming/bond breaking bond lengths and compare the structure to the one you optimized in section (b).

'''Note''' For calculations using the redundant coord editor. Once the calculations have been run; due a bug which was caused by a recent update in gaussian. You may get an error saying 'bad data line x' in the .chk point file. by convention gausview uses the .chk to open for the next step, but this will not open due to the error, the output is a binary file, so it becomes very difficult to find and fix. This file contains more data, particularly orbital data. However for this section we just need the geometries to continue which are sorted in the human readable log file which is still produced with no error in the output. Therefor if you get this error continue to the next step with log file. A new .chk file will be produced in the next step. [[User:NF710|NF710]] ([[User talk:NF710|talk]]) 14:01, 29 October 2015 (BST)

 

(e) Now we will optimize the boat transition structure. We will do this using the '''QST2''' method. In this method, you can specify the reactants and products for a reaction and the calculation will interpolate between the two structures to try to find the transition state between them. You must make sure that your reactants and products are numbered in the same way. Therefore, although our reactants and products are both 1,5-hexadiene, we will need to manually change the numbering for the product molecule so that it corresponds to the numbering obtained if our reactant had rearranged.

e.g.

<center>[[Image:pic3.jpg|200px]]</center>

Open the chk file corresponding to the optimized Ci reactant molecule (''anti2'' in [[Mod:phys3#Appendix 1|Appendix 1]]). Now open a second window and create a new MolGroup. Copy the optimized reactant molecule into the new window. In the same window, now select '''File → New → Add to MolGroup'''. The original molecule should disappear and a green circle should appear at the top left-hand corner with a '''2''' next to it. Clicking on the down arrow by the '''2''' will take you back to the original window and you will see your molecule again. This is how we read multiple geometries into GaussView. Go back to window '''2''', and copy and paste the reactant molecule a second time. This is going to be the product molecule and will be the molecule on which we need to change the numbering. If you now click on the icon showing two molecules side by side, then you can view both molecules simultaneously.

Now go to the '''View''' menu and select '''Labels''' so that you can see the numbering on both structures. Orient the two structures separately so they look something like the following:

{| align="center"
|- align="center"
|
[[Image:pic4a.jpg|200px]]
|
[[Image:pic4b.jpg|200px]]
|- align="center"
| align="center" | ''Reactant''
| align="center" | ''Product''
|}

 

Now click on the product structure. Go to the '''Edit''' menu and select '''Atom List'''. Starting from Atom 1 on the reactant, go through and renumber all the atoms on the Product so that they match the reactant molecule, e.g. for the numbering above you would start by changing atom '''6''' on the product molecule to atom '''3'''. The other atom numbers will update as you do this so make sure you do it in the correct order. (Note: Start numbering at 1 and go up, i.e. do not order 5 before 3 to avoid problems with the numbers updating --[[User:Jrc10|Jrc10]] 15:13, 31 January 2013 (UTC)) At the end, the numbering on your two molecules should correspond to each other in the following way:

 

{| align="center"
|- align="center"
|
[[Image:pic5a.jpg|200px]]
|
[[Image:pic5b.jpg|200px]]
|- align="center"
| align="center" | ''Reactant''
| align="center" | ''Product''
|}

 

Now we will set up the first '''QST2''' calculation. Go to the '''Gaussian''' menu and select '''Job Type''' as '''Opt+Freq''', and optimize to a transition state. This time you will have two options - '''TS (Berny)''' which we used in the previous calculations and '''TS (QST2)'''. Select '''TS (QST2)'''. Submit the job.

You will find that the job fails. To see why, open the chk file you created and view the structure. You will see that it looks a bit like the chair transition structure but more dissociated. In fact when the calculation linearly interpolated between the two structures, it simply translated the top '''allyl''' fragment and did not even consider the possibility of a rotation around the central bonds. It is clear that the QST2 method is never going to locate the boat transition structure if we start from these reactant and product structures.

Now go back to the original input file where you set up your QST2 calculation. We will now modify the reactant and product geometries so that they are closer to the boat transition structure. Click on the reactant molecule first and select the central '''C-C-C-C''' dihedral angle (i.e. '''C2-C3-C4-C5''' for the molecule above) and change the angle to 0o. Then select the inside '''C-C-C''' (i.e. '''C2-C3-C4''' and '''C3-C4-C5''' for the molecule above) and reduce them to 100o. Do the same for the product molecule. Your reactant and product molecules should now look like the following:

 

{| align="center"
|- align="center"
|
[[Image:pic6a.jpg|200px]]
|
[[Image:pic6b.jpg|200px]]
|- align="center"
| align="center" | ''Reactant''
| align="center" | ''Product''
|}

 

Set up the QST2 calculation again, renaming both the chk file under '''Link 0''' and the input file. Run the job again. This time it should converge to the boat transition structure. Check that there is only one imaginary frequency and visualize its motion.

The object of this exercise is to illustrate that although the QST2 method is has some advantages because it is fully automated, it can often fail if your reactants and products are not close to the transition structure. There is another method, the '''QST3''' method, that allows you to input the geometry of a guess transition structure also and this can often be more reliable. If you have time, you can try generating a guess boat transition structure and see if you can get the calculation to converge using the original reactant and product molecules. Remember to check the atom numbers in the transition structure are in the right order.

 

(f) Take a look at your optimized chair and boat transition structures. Which conformers of 1,5-hexadiene do you think they connect? You will find that it is almost impossible to predict which conformer the reaction paths from the transitions structures will lead to. However, there is a method implemented in Gaussian which allows you to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface. This is called the '''Intrinsic Reaction Coordinate''' or '''IRC''' method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Open the chk file for one of your optimized chair transition structures. Under the '''Gaussian''' menu, select '''IRC''' under the '''Job Type''' tab. You will be presented with a number of options. The first is to decide whether to compute the reaction coordinate in one or both directions. As our reaction coordinate is symmetrical, we will only choose to compute it in the forward direction. Normally you would do both forward and reverse, either in one job or in two separate jobs. You are also given the option to calculate the force constants once, at every step along the IRC or to read them from the chk file, in this case choose calculate always. You would use the latter option if you have previously run a frequency calculation.

The final option to consider is the number of points along the IRC. The default is '''6''' but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under '''Link 0''' and submit the job. The job will take a while so now is a good time to take a coffee break...

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the '''B3LYP/6-31G*''' level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different.

As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program '''FreqChk''' to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The '''FreqChk''' utility program can be accessed from '''Gaussian09W'''. Launch '''Gaussian09W'''. Select '''utilities''' from the menu and click on '''FreqChk''' to launch the utility program. You will be prompted for a chk file. Follow the instructions from this [http://www.gaussian.com/g_tech/g_ur/u_freqchk.htm web link] to proceed.

 

=== Appendix 1 ===

 

'''Note:''' 3D models of all the conformers in the table below are given [[Mod:phys3_appendix1|here]].

 

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees HF/3-21G'''
| width="200" | '''Relative Energy/kcal/mol'''
|- align="center"
| ''gauche''
|
[[Image:gauche1.jpg|150px]]
| C2
| -231.68772
| 3.10
|- align="center"
| ''gauche2''
|
[[Image:gauche2.jpg|150px]]
| C2
| -231.69167
| 0.62
|- align="center"
| ''gauche3''
|
[[Image:gauche3.jpg|150px]]
| C1
| -231.69266
| 0.00
|- align="center"
| ''gauche4''
|
[[Image:gauche4.jpg|150px]]
| C2
| -231.69153
| 0.71
|- align="center"
| ''gauche5''
|
[[Image:gauche5.jpg|150px]]
| C1
| -231.68962
| 1.91
|- align="center"
| ''gauche6''
|
[[Image:gauche6.jpg|150px]]
| C1
| -231.68916
| 2.20
|- align="center"
| ''anti1''
|
[[Image:anti1.jpg|150px]]
| C2
| -231.69260
| 0.04
|- align="center"
| ''anti2''
|
[[Image:anti2.jpg|150px]]
| Ci
| -231.69254
| 0.08
|- align="center"
| ''anti3''
|
[[Image:anti3.jpg|150px]]
| C2h
| -231.68907
| 2.25
|- align="center"
| ''anti4''
|
[[Image:anti4.jpg|150px]]
| C1
| -231.69097
| 1.06
|}

 

=== Appendix 2 ===

{| cellpadding="5"
|- align="center"
|
[[Image:appendix2a.jpg|300px]]
|- align="center"
| ''C2h Chair Transition State''
|- align="center"
|- align="center"
|- align="center"
|
[[Image:appendix2b.jpg|300px]]
|- align="center"
| ''C2v Boat Transition State''
|}

 

=== Results Table ===

 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

 

==The Diels Alder Cycloaddition==

''In this exercise, you will characterise transition structures using any of the methods described above in the tutorial: the choice is up to you. In addition, you will look at the shape of some of the molecular orbitals. To help you structure your report, there is a data/discussion sheet at the end of this section.''

 

[[Image:mb_da1.jpg |right|thumb|Diels Alder cycloaddition]]
The Diels Alder reaction belongs to a class of reactions known as pericyclic reactions. The π orbitals of the dieneophile are used to form new σ bonds with the π orbitals of the diene. Whether or not the reactions occur in a concerted stereospecific fashion ('''allowed''') or not ('''forbidden''') depends on the number of π electrons involved. In general the HOMO/LUMO of one fragment interacts with the HOMO/LUMO of the other reactant to form two new bonding and anti-bonding MOs. The nodal properties allow one to make predictions according to the following rule:

''If the HOMO of one reactant can interact with the LUMO of the other reactant then the reaction is '''allowed'''.''

''The HOMO-LUMO can only interact when there is a significant overlap density. If the orbitals have different symmetry properties then no overlap density is possible and the reaction is '''forbidden'''.''

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

 

Shown on the right is a diagram of the transition state for the Diels-Alder reaction between ethylene and butadiene. The ethylene approaches the cis form of butadiene from above.
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]

Before beginning our quantitative study, it is helpful to discuss the interaction of the π orbitals in a simple qualitative way.

''You will confirm some of these considerations in your computations.''

The principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] since one has 4 π orbitals in the π system of butadiene. The orbitals of ethylene and butadiene and ethylene can be classified as symmetric '''s''' or anti-symmetric '''a''' with respect to the plane of symmetry shown.

The HOMO of ethylene and the LUMO of butadiene are both '''s''' (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both '''a'''. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is '''a'''.

 

=== Exercise ===

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

i) Use GaussView to build cis butadiene, and optimize the geometry using Gaussian. Plot the HOMO and LUMO of cis butadiene and determine its symmetry (symmetric or anti-symmetric) with respect to plane.

''There are two ways to do this in GaussView. One is: Select '''Edit→MOs'''. Select the HOMO and the LUMO from the MO list (highlights it yellow). Click the button '''Visualise''' (not Calculation), then '''Update'''. Alternately, having calculated the surface for this orbital, you can display it in the main GaussView window for the molecule, from the '''Results→Surfaces''' menu. Select '''Surface Actions→Show Surface'''. Having displayed the surface this way, you can also select '''View→Display Format→Surface''', and change '''Solid''' to '''Mesh'''.''

 

ii) Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

[[Image:mb_da3.jpg |right|thumb|]]

The transition structure has an envelope type structure, which maximizes the overlap between the ethylene π orbitals and the π system of butadiene. One way to obtain the starting geometry is to build the bicyclo system (b) and then remove the -CH2-CH2- fragment. One must then guess the interfragment distance (dashed lines) and optimize the structure, but use any method you wish, based on the tutorial above, to characterise the transition structure. Confirm you have obtained a transition structure for the Diels Alder reaction!

[[Image:mb_da4.jpg |right|thumb|guessing the transition structure]]

Once you have obtained the correct structure, plot the HOMO as in (i). Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

 

(iii) To Study the regioselectivity of the Diels Alder Reaction

Cyclohexa-1,3-diene '''1''' undergoes facile reaction with maleic anhydride '''2''' to give primarily the endo adduct. The reaction is supposed to be kinetically controlled so that the exo transition state should be higher in energy.

[[Image:Bearpark_pic_edit_by_jm906.JPG |right|thumb|regioslectivity]]

Locate the transition structures for both 3 and 4. Compare the energies of the endo and exo forms.

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?

 

=== Discussion ===

Use this template as a guide. Screen images can be saved from the GaussView '''File''' menu.

''For cis butadiene'': 
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

''For the ethylene+cis butadiene transition structure'': 
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state.
Is the formation of the two bonds synchronous or asynchronous?
How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure '''s''' or '''a'''?

Which MOs of butadiene and ethylene have been used to form this MO?
Explain why the reaction is allowed.

''For the cyclohexa-1,3-diene reaction with maleic anhydride'': 
Give the relative energies of the exo and endo transition structures.
Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so-called “secondary orbital overlap effect”?
(There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

''Further discussion'': 
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time.
(e.g. {{DOI|10.1021/jo0348827}})

----


© 2008-2013, Imperial College London

Rep:Mod:somethingsomething

2015-11-30T13:50:23Z

Mjbear: Created page with "test edit --~~~~"

test edit
--[[User:Mjbear|Mjbear]] ([[User talk:Mjbear|talk]]) 13:50, 30 November 2015 (UTC)

Mod:writeup

2015-10-22T21:25:36Z

Mjbear: /* Submitting your report */

See also: [[Mod:Cheatsheet|Cheatsheet]].

== The expected length of the report ==
A Wiki does not have pages as such. But as a very rough guide, expect to produce something the equivalent of about six printed pages (although you can invoke ''pop-ups'' and the like which make a page count only very approximate). Use graphics reasonably sparingly, and to the point.

= Why Wiki? =
Since everyone is used to using [http://www.wordonwiki.com Microsoft Word], why do we [[talks:rzepa2011|use a Wiki]] for this course? Well, the Wiki format has several advantages.
#A full revision and fully dated history across sessions is kept (Word only keeps this during a session). This is more suited for laboratory work, where you indeed might need to go back to a particular day and experiment to check your notes.
#The (chemistry) Wiki allows you to include molecule coordinates, vibrations and MO surfaces which can be rotated and inspected, along with other chemical extensions. Word does not offer this.
#The Wiki allows you to include "zoomable" graphics in the form of SVG (which Gaussview generates), and access to the 17-million large [http://commons.wikimedia.org/wiki/Main_Page WikiCommons] image library, as well as access to the Wikipedia InterWiki.
#The [[w::Help:Template|template]] concept allows pre-formated entry. There are lots of powerful [[w:Category:Chemical_element_symbol_templates|chemical templates]] available.
#Autonumbered referencing, and particularly cross-referencing, is actually easier than using Word.
#You (and the graders) can access your report anywhere online, it is not held on a local hard drive which you may not have immediate access to.
#It has automatic date and identity stamps for ALL components, which means we can assess that part of the report handed in by any deadline, and deal separately with anything which has a date-stamp past a given deadline. A Word document has only a single date-and-time stamp and so deadlines must apply to the whole document.
#And we have been using Wikis for course work since '''2006''', so there is lots of expertise around!
#And finally, Wiki is an example of a [http://en.wikipedia.org/wiki/Markdown MarkDown] language, one designed to facilitate writing using an easy-to-read, easy-to-write plain text format (with the option of converting it to structurally valid XHTML).

=Report Preparation =

== Before you start writing ==
Before you start writing, you might wish to read this article<ref name="adma.200400767">G.M. Whitesides, "Whitesides' Group: Writing a Paper", ''Advanced Materials'', '''2004''', ''16'', 1375–137 {{DOI|10.1002/adma.200400767}}</ref> (or perchance this advice<ref name="ac2000169">R. Murray, "Skillful writing of an awful research paper", ''Anal. Chem.'', '''2011''', ''83'', 633. {{DOI|10.1021/ac2000169}}</ref>). In your report you should discuss your evaluation of each of the techniques you use here. You should include at least '''three literature references in addition to the ones given here'''. You might also want to check the [[Mod:latebreak|late breaking news]] to see if there are any helpful hints about the project you might want to refer to. You will be writing your report in Wiki format, and it is best to do this continually as you do the experiment. In effect, your Wiki report is also your laboratory manual.

#[[File:Wiked.jpg|right|400px|WikED editor]]Open Firefox as a Web browser.
#There should be a tab for the course Wiki, but if not, use the URL '''www.ch.ic.ac.uk'''
#*[[Image:exception1.jpg|right|thumb|Security exception]]If the browser asks you to add a security exception, do so and proceed to '''view/confirm''' the certificate.
#You can view the Wiki without logging in, but to create a report, you will have to login as yourself. Check '''Remember my login on this computer'''
#Before you start, you might want to visit the [[Special:Preferences|preferences]] page to customise the Wiki for yourself.
#Follow the procedures below. Check that the WikED icon is present at the top, just to the right of the log out text (ringed in red). If you want a minimalist editing interface, click this icon to switch it off. A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.

=== Assigning your report an identifier ===
#*[[Image:New_report.jpg|right|400px|Creating a report page]] In the address box, type something like
#**'''wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:{{fontcolor1|yellow|black|XYZ1234}}'''
#*The characters '''Mod''' indicate a report associated with the modelling course, and '''{{fontcolor1|yellow|black|XYZ1234}}''' is your secret password for the report. It can be any length, but do not make it too long! It should then tell you there is no text in this page. If not, try another more unique password. You should now click on the '''edit this page''' link to start. Use a different address for each module of the course you are submitting.
#*It is a {{fontcolor1|yellow|black|good idea}} to add a bookmark to this page, so that you can go back to it quickly.
==== Assigning your report a persistent (DOI-style) identifier.====
Use [http://spectradspace.lib.imperial.ac.uk/url2handle/ this tool] to assign a shorter identifier for your report (one that can be invoked using eg <nowiki>{{DOI|shortidentifier]]</nowiki>.

=== Converters to the Wiki format ===
#Convert a Word document. Open it in '''OpenOffice''' (rather than the Microsoft version) and '''export''' as Mediawiki. Open the resulting .txt file in eg WordPad, select all the text, copy, and then paste this into the Wiki editing page. You will still have to upload the graphical images from the original Word document separately.
#There is also a [http://labs.seapine.com/htmltowiki.cgi HTML to Wiki] converter which you can use to import HTML code from an existing Web page into a (Media)Wiki.

== Basic editing ==
An [[Mod:inorganic_wiki_page_instructions|introductory tutorial]] is available which complements the information here.
*A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.
*[[Image:report12345.jpg|right|thumb|The editing environment]]You will need to create a separate report page on this Wiki for each module of the course. Keep its location private (i.e. do not share the URL with others).
*The WikED toolbar along the top of the page has a number of tools for:
**adding citation references,
**superscript and subscripting (the H2O WikEd symbol will automatically do this for a formula),
**creating tables
**adding links (Wiki links are internal, External links do what they say on the tin)
**# local to the wiki, as <nowiki>[[mod:writeup|text of link]]</nowiki>
**# remote, as <nowiki>[http://www.webelements.com/ text of link]</nowiki>
**# Interwiki, as <nowiki>[[w:Mauveine|Mauveine]]</nowiki>
**# DOI links are invoked using the DOI template <nowiki>{{DOI|..the doi string ..}}</nowiki> or the more modern form <nowiki>[[doi:..the dpi string..]]</nowiki>
**# Links to an Acrobat file you have previously uploaded to the Wiki can be invoked using this template: <nowiki>{{Pdf|tables_for_group_theory.pdf|...description of link ...}}</nowiki>
**# There are lots of other [[Special:UncategorizedTemplates|templates]] to make your life easier such as the [[w:Template:Chembox|ChemBox]]
**If you need some help, invoke it from the left hand side of this page.
*Upload all graphics files also with unique names (so that they do not conflict with other people's names). If you are asked to replace an image, '''REFUSE''' since you are likely to be over-writing someone else's image!
** Invoke such an uploaded file as <nowiki>[[image:nameoffile.jpg|right|200px|Caption]] </nowiki>
**We support WikiComons, whereby images from the [http://commons.wikimedia.org/wiki/Main_Page content (of ~10 million files)] from [http://meta.wikimedia.org/wiki/Wikimedia_Commons Wikimedia Commons Library] can be referenced for your own document. If there is a name conflict, then the local version will be used before the Wiki Commons one.
***To find a file, go to [http://commons.wikimedia.org/wiki/Main_Page Commons]
***Find the file you want using the search facility
***Invoke the top menu, '''use this file in a Wiki''', and copy the string it gives you into your Wiki page
*** <nowiki>[[File:Armstrong Edward centric benzene.jpg|thumb|Armstrong Edward centric benzene]]</nowiki>
*Colour can be added (sparingly) using this {{fontcolor1|yellow|black|text fontcolor}} template. (invoked as <nowiki>{{fontcolor1|yellow|black|text fontcolor}}</nowiki> )
*Save and preview constantly (this makes a new version, which you can always revert to). It goes without saying that you should not reference this page from any other page, or indeed tell anyone else its name.
*'''Important:''' Every 1-2 hours, you might also want to make a [[Mod:writeup#Backing_up_your_report|backup of your report]]. This is particularly important when adding Jmol material, since any error in the pasted code can result in XML errors. The current Wiki version does not flag these errors properly, but instead just hangs the page. Whilst you can try to [[Mod:writeup#Fixing_broken__Pages|repair the page]] as described below, it is much safer to also have a backup!
*You should get into the habit of recording results, and appropriate discussion, soon after they are available, in the manner of a laboratory note book.

== More Editing features ==
=== Handling References/citations with a DOI ===
This section shows how literature citations<ref name="jp027596s">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343. {{DOI|10.1021/ja9825332}}</ref> can be added to text<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref> using the '''<nowiki>{{DOI|value}}</nowiki>''' (digital object identifier) template to produce a nice effect. Citations can be easily added from the WikED toolbar.
*The following text is added to the wiki, exactly as shown here: '''<nowiki><ref name="ja9825332">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343.{{DOI|10.1021/ja9825332}}</ref></nowiki>'''
*Giving a reference a unique identifier, such as '''<nowiki><ref name="ja9825332"></nowiki>''' allows you to refer to the same footnote again by using a ref tag with the same name. The text inside the second tag doesn't matter, because the text already exists in the first reference. You can either copy the whole footnote, or you can use a terminated empty ref tag that looks like this: '''<nowiki><ref name="ja9825332" /></nowiki>'''.
*Collected citations will appear below wherever you place the '''<nowiki><references /></nowiki>''' tag, as here. If you forget to include this tag, the references will not appear!
==== Including the DOI for your experiment data ====
The datasets associated with your experiment can be given a DOI by '''publishing''' any entry in the [https://scanweb.cc.imperial.ac.uk/uportal2/ SCAN Portal]. You can include this DOI as a normal citation.<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref>

==== Additional citation handling ====
* A macro-based reference formatting program has been developed in Microsoft Excel to not only produce the wiki code for direct pasting into your report, but that '''''also''''' formats text for placing in documents, such as synthesis lab reports. This program is available [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Reference_Formatting_Program here].
* A '''[[Template:Cite_journal|Cite journal]] template''' is installed for anyone who wants to experiment
----

References and citations
<references />

----

=== Using an iPad ===

[https://itunes.apple.com/gb/app/wiki-edit/id391012741?mt=8 Wiki Edit] for IOS allows a Wiki to be edited using an iPad. You can dictate your text using '''Siri''' if your speed at '''thumb-typing''' is not what it should be.

= Bringing your report to life =
== Basic JSmol ==
You can use coordinate files created as part of your work (in CML or Molfile format) to insert rotating molecules for your page.
#Using your graphical program (ChemBio3D or Gaussview), '''save''' your molecule as an '''MDL File''', which has the extension '''.mol''', or as '''chemical markup language''', which has the extension '''.cml'''.
#Or, if your calculation ran on the SCAN batch system, '''publish''' the calculation, and in the resulting deposited space, download the .cml or the '''logfile.out''' file to be found there (the latter should be used for vibrations only).
#On the Wiki, '''Upload File''' (from the left hand panel) and select the molecule file you have just placed on your hard drive as above.
#On your Wiki page, insert <nowiki><jmolFile text="Explanatory text for link">BCl3-09.log</jmolFile></nowiki> where in this example, BCl3-09.log is the just uploaded file.
##The should produce <jmolFile text="this link">BCl3-09.log</jmolFile>. When clicked, it will open up a separate floating window for your molecule.
##Further actions upon the loaded molecule (such as selecting a vibrational mode and animating the vibration) are done by right-mouse clicking in the Jmol window.

#When using animations, please let them pop up in a separate window using the <jmolAppletButton> function. Your browser won't slow down and you will make your life so much simpler. =)
##Read more on how to do that [http://wiki.jmol.org/index.php/MediaWiki#Jmol_applet_in_a_popup_window here ]. --[[User:Rea12|Rea12]] 20:58, 8 September 2014 (BST)

== Advanced JSmol ==

A much more powerful invocation is as follows. The following allows a molecule to be directly embedded into the report, and it also shows how to put a script in to control the final display.
{| class="wikitable" border="2"
|-
! copy/paste either of the two sections below into your own Wiki
|-
|<pre><jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>yourmolecule.cml</uploadedFileContents>
</jmolApplet>
</jmol>


<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script><uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol></pre>
|-
! First molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])
|-
|<jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color><size>300</size>
<script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script>
<uploadedFileContents>pentahelicene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Second molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])

|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script>
<uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Every time you embed a molecule in a Wiki page in the above manner, the Web browser must set aside memory. Too many molecules, and the memory starts to run out, and the browser may slow down significantly. So use the feature sparingly, only including key examples where some structural feature would benefit from the rotational capabilities.
It is [http://chemapps.stolaf.edu/jmol/docs/ possible] to add many other commands to the JSmol container above. For example, '''<nowiki><script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script></nowiki>''' will colour atoms 3 4 and 5 (obtained by mouse-overs) purple, and then measure the length of the 3-5 bond. Further examples of how to invoke Jmol are [http://www.mediawiki.org/wiki/Extension:Jmol#Installing_Jmol_Extension found here], and a comprehensive list [http://chemapps.stolaf.edu/jmol/docs/ given here].

== Incorporating orbital/electrostatic potential isosurfaces ==
The procedure is as follows
# Run a Gaussian calculation on the SCAN
# When complete, select ''Formatted checkpoint file'' from the output files and download
# Double click on the file to load into Gaussview
##To generate a molecule orbital, '''Edit/MOs''' and select (= yellow) your required orbitals.
##* '''Visualise''' and '''Update''' to generate them
## To generate an electrostatic potential, '''Results/Surfaces and Contours''', then '''Cube Actions/New Cube/Type=ESP'''. This will take 2-3 minutes to generate
##* In '''Surfaces available''' pre-set the Density to '''0.02''' and then '''Surface Actions/New Surface'''. Try experimenting with the value of Density for the best result. Save the cube as per below.
# In '''Results/Surfaces and contours''' from the '''cubes available''' list, select one and '''Cube actions/save cube'''
# Invoke [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ this page] and you will be asked to select your cube file,
# followed by three file save dialogs, one for the coordinates (.xyz), one for the MO surface (.jvxl) and a shrink-wrapped bundle (.pngj).
# Insert the following code into your Wiki, replacing the file name with your own choice from the preceding file save dialogs.
<pre><nowiki><jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol></nowiki>
</pre>
# [[image:absolute_path.jpg|right|350px]]Next, upload these two files into the Wiki (one file at a time, the multiple file uploader does not seem to work for this task)
## Now for the tough bit. You will need to find the absolute path for the .jvxl file. Above, this appears as images/1/1b/AHB_mo22-2.cub.jvxl
## Just after uploading a .jvxl file, you will see a response as shown on the right.
## Right click on '''Edit this file using an external application'''. You can used any text editor (Wordpad etc).
## This text file will contain something like: <tt>; or go to the URL <nowiki>https://wiki.ch.ic.ac.uk/wiki/images/1/1b/AHB_mo22-2.cub.jvxl</nowiki></tt>
#Select just the string '''images/1/1b/AHB_mo22-2.cub.jvxl''' and paste it in as shown above:
#You should get something akin to:
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;
</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
* You can superimpose two surfaces. Change the script contents above to append a second surface to the first: <pre><script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;isosurface append color red blue "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script></pre>
* The four colours used in this line can be changed to whatever you consider appropriate.
=== An alternative way of loading surfaces ===
This method avoids the need to specify paths to files as seen above. Instead uses the '''.pngj''' bundle which contains all necessary information and can be invoked by
<pre><nowiki><jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile></nowiki></pre> which produces <jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile>.
# It only supports one surface (you cannot superimpose two orbitals)
# You can also load other surfaces, such as <jmolFile text="molecular electrostatic potentials">Checkpoint_60018_esp.cub.pngj‎</jmolFile> generated from a cube of electrostatic potential (ESP) values created using Gaussview as follows:
## Download .fchk file from SCAN
## Open using Gaussview
## '''Results/Surfaces & contours/Cube actions/New Cube/ESP''' and then '''cube actions/save cube''' which is how the above was generated. You may have to play around with the value of the density (~0.02).

=== MOPAC orbitals ===
# Run MOPAC from ChemBio3D, selecting '''Compute Properties/Molecular Surface''' from the '''properties''' pane, and in the '''General pane''' specify a location for the output and deselect '''Kill temporary files''' if not already so.
# Upload the '''.mgf''' file so produced to the Wiki
# Invoke as follows ('''MO 35;''' means the 35th most stable orbital for that molecule).
<pre><nowiki><jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>300</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol></nowiki></pre>
<jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>200</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol>

== Enhancing your report with Equations ==
*You may have need to express some [http://meta.wikimedia.org/wiki/Help:Formula equations] on the Wiki. This is currently supported only using a notation derived from '''LaTeX''', and as with the Jmol insertion above, is enabled within a '''<nowiki><math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math></nowiki>''' field inserted using the default editor (the SQRT(n) button), and producing the following effect:
<math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math>

The requisite syntax can be produced by using
*MathType as an equation editor (used standalone or in Word). It places the required LaTeX onto the clipboard for pasting into the Wiki).
*[http://www.lyx.org/ Lyx] which is a free stand-alone editor.
*A more general solution to this problem is simply to create a graphical image of your equation, and insert that instead as a picture.

== Inserting Tables ==
Instead of inserting screenshots of Excel, tables can be produced using MediaWiki markup (see [http://www.mediawiki.org/wiki/Help:Tables this page]), where you can also find lots of examples of different styles of table. However, this can be quite time consuming when you have a lot of tabulated data and need to copy it from somewhere like Excel into ChemWiki. Instead of typing it by hand, you can save your Excel worksheet as a comma separated file (.csv) and then use this [[http://area23.brightbyte.de/csv2wp.php CSV to MediaWiki markup]] convertor. Note that cells starting with "-", e.g. for negative numbers, need a space inserted between the - and | in the output otherwise MediaWiki interprets it as a new row.

Another web-based utility is available called [http://excel2wiki.net/ Excel2Wiki] which can be used to generate MediaWiki code from an Excel table.

== SVG (for display of IR/NMR/Chiroptical Spectra) ==
[[File:IR.svg|300px|right|SVG]]SVG stands for '''scaleable-vector-graphics'''. Its advantage is well, that it scales properly (but it has many others, including the ability to make simple edit to captions etc using Wordpad or similar). From your point of view, it is readily generated using Gaussview. If you view an '''IR/NMR/UV-vis/IRC/Scan/''' spectrum in this program, it allows you to export the spectrum as SVG (right-mouse-click on the spectrum to pull down the required menu). Upload this file, and invoke it as <nowiki>[[File:IR.svg|200px|right|SVG]]</nowiki> If you open eg IR.svg in Wordpad (or other text editor), you can edit the captions, font sizes etc (its fairly obvious). Oh, you will need to use a web browser that actually displays SVG. Internet Explorer 8 does not (9 is supposed to). Use Firefox/Chrome/Safari etc.

== Chemical Templates ==
An example is the [[w:Template:Chembox|ChemBox]]. Volunteers needed to test/extend these!

= Submitting your report =


--[[User:Mjbear|Mjbear]] ([[User talk:Mjbear|talk]]) 22:24, 22 October 2015 (BST)

For the '''Computational Chemistry Lab''': submit your wiki URL address on Blackboard by 12:00 on the friday of the 2-week experiment.
The link is here: https://bb.imperial.ac.uk/webapps/blackboard/content/listContentEditable.jsp?content_id=_705671_1&course_id=_8223_1&content_id=_705733_1

= Backing up your report =
[[Image:export1.jpg|left|250px]][[Image:Export2.jpg|right|200px]]Invoke [[Special:Export|this utility]] to back your project up. In the box provided, enter e.g. '''Mod:wzyz1234''' being the password for your report. This will generate a page (right) which can be saved using the Firefox '''File/Save_Page_as''' menu. Specify '''Web Page, XML only''' as the format, and add .xml to the file suffix. You might want to do this eg on a daily basis to secure against corruption. This is in addition to the notes for how to repair broken pages.

The same file can now be reloaded using [[Special:Import|Import]].

= Fixing broken Pages =
There are several ways in which a page can break.

*We have had instances of people inserting a corrupted version of the Jmol lines into their project, resulting in a '''XML error''' or '''Database error'''. Recovering from such an error is not simple. So we do ask that you carefully check what you are pasting into the Wiki, and that its form is exactly as shown above. For example, below is a real example of inducing such an error. Can you see where the fault lies? (Answer: the <nowiki><jmol></nowiki> tag is not matched by <nowiki></jmol></nowiki>. If tags are not balanced, XML errors will occur).
<pre><jmol><jmolApplet><title>equatorial</title><color>white</color>
<size>200</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Pl506_14_equatorial.mol</uploadedFileContents></pre>
*Another example might be wish to indicate a citation using <nowiki><ref>...details </ref></nowiki> but in fact end up entering <nowiki><ref> ...</nowiki> (i.e. missing out the <nowiki></ref></nowiki>)
*If you do encounter such an error, try invoking your project as '''<nowiki>https://www.ch.ic.ac.uk/wiki/index.php?title=Mod:wzyz1234&action=history</nowiki>''' and edit and then save an uncorrupted version. You will need to be already logged in before you attempt to view the history in this way, since logging in '''after''' you invoke the above will return you not to the history, but to the corrupted page (Hint: it sometimes helps to check '''Remember my login on this computer''' as you log in). For example, the history for this page can be seen [https://www.ch.imperial.ac.uk/wiki/index.php?title=Mod:writeup&action=history here]. You can eg load this preceeding page, and then use it to replace '''writeup''' with your own project address.
*If the preceeding does not work try the instructions shown [[mod:fix|here]].

= Feedback =
Each Wiki page has a discussion section, including your submitted report page. 

See also: [[Mod:Cheatsheet|cheatsheet]]

Mod:writeup

2015-10-22T21:24:40Z

Mjbear: /* Submitting your report */

See also: [[Mod:Cheatsheet|Cheatsheet]].

== The expected length of the report ==
A Wiki does not have pages as such. But as a very rough guide, expect to produce something the equivalent of about six printed pages (although you can invoke ''pop-ups'' and the like which make a page count only very approximate). Use graphics reasonably sparingly, and to the point.

= Why Wiki? =
Since everyone is used to using [http://www.wordonwiki.com Microsoft Word], why do we [[talks:rzepa2011|use a Wiki]] for this course? Well, the Wiki format has several advantages.
#A full revision and fully dated history across sessions is kept (Word only keeps this during a session). This is more suited for laboratory work, where you indeed might need to go back to a particular day and experiment to check your notes.
#The (chemistry) Wiki allows you to include molecule coordinates, vibrations and MO surfaces which can be rotated and inspected, along with other chemical extensions. Word does not offer this.
#The Wiki allows you to include "zoomable" graphics in the form of SVG (which Gaussview generates), and access to the 17-million large [http://commons.wikimedia.org/wiki/Main_Page WikiCommons] image library, as well as access to the Wikipedia InterWiki.
#The [[w::Help:Template|template]] concept allows pre-formated entry. There are lots of powerful [[w:Category:Chemical_element_symbol_templates|chemical templates]] available.
#Autonumbered referencing, and particularly cross-referencing, is actually easier than using Word.
#You (and the graders) can access your report anywhere online, it is not held on a local hard drive which you may not have immediate access to.
#It has automatic date and identity stamps for ALL components, which means we can assess that part of the report handed in by any deadline, and deal separately with anything which has a date-stamp past a given deadline. A Word document has only a single date-and-time stamp and so deadlines must apply to the whole document.
#And we have been using Wikis for course work since '''2006''', so there is lots of expertise around!
#And finally, Wiki is an example of a [http://en.wikipedia.org/wiki/Markdown MarkDown] language, one designed to facilitate writing using an easy-to-read, easy-to-write plain text format (with the option of converting it to structurally valid XHTML).

=Report Preparation =

== Before you start writing ==
Before you start writing, you might wish to read this article<ref name="adma.200400767">G.M. Whitesides, "Whitesides' Group: Writing a Paper", ''Advanced Materials'', '''2004''', ''16'', 1375–137 {{DOI|10.1002/adma.200400767}}</ref> (or perchance this advice<ref name="ac2000169">R. Murray, "Skillful writing of an awful research paper", ''Anal. Chem.'', '''2011''', ''83'', 633. {{DOI|10.1021/ac2000169}}</ref>). In your report you should discuss your evaluation of each of the techniques you use here. You should include at least '''three literature references in addition to the ones given here'''. You might also want to check the [[Mod:latebreak|late breaking news]] to see if there are any helpful hints about the project you might want to refer to. You will be writing your report in Wiki format, and it is best to do this continually as you do the experiment. In effect, your Wiki report is also your laboratory manual.

#[[File:Wiked.jpg|right|400px|WikED editor]]Open Firefox as a Web browser.
#There should be a tab for the course Wiki, but if not, use the URL '''www.ch.ic.ac.uk'''
#*[[Image:exception1.jpg|right|thumb|Security exception]]If the browser asks you to add a security exception, do so and proceed to '''view/confirm''' the certificate.
#You can view the Wiki without logging in, but to create a report, you will have to login as yourself. Check '''Remember my login on this computer'''
#Before you start, you might want to visit the [[Special:Preferences|preferences]] page to customise the Wiki for yourself.
#Follow the procedures below. Check that the WikED icon is present at the top, just to the right of the log out text (ringed in red). If you want a minimalist editing interface, click this icon to switch it off. A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.

=== Assigning your report an identifier ===
#*[[Image:New_report.jpg|right|400px|Creating a report page]] In the address box, type something like
#**'''wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:{{fontcolor1|yellow|black|XYZ1234}}'''
#*The characters '''Mod''' indicate a report associated with the modelling course, and '''{{fontcolor1|yellow|black|XYZ1234}}''' is your secret password for the report. It can be any length, but do not make it too long! It should then tell you there is no text in this page. If not, try another more unique password. You should now click on the '''edit this page''' link to start. Use a different address for each module of the course you are submitting.
#*It is a {{fontcolor1|yellow|black|good idea}} to add a bookmark to this page, so that you can go back to it quickly.
==== Assigning your report a persistent (DOI-style) identifier.====
Use [http://spectradspace.lib.imperial.ac.uk/url2handle/ this tool] to assign a shorter identifier for your report (one that can be invoked using eg <nowiki>{{DOI|shortidentifier]]</nowiki>.

=== Converters to the Wiki format ===
#Convert a Word document. Open it in '''OpenOffice''' (rather than the Microsoft version) and '''export''' as Mediawiki. Open the resulting .txt file in eg WordPad, select all the text, copy, and then paste this into the Wiki editing page. You will still have to upload the graphical images from the original Word document separately.
#There is also a [http://labs.seapine.com/htmltowiki.cgi HTML to Wiki] converter which you can use to import HTML code from an existing Web page into a (Media)Wiki.

== Basic editing ==
An [[Mod:inorganic_wiki_page_instructions|introductory tutorial]] is available which complements the information here.
*A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.
*[[Image:report12345.jpg|right|thumb|The editing environment]]You will need to create a separate report page on this Wiki for each module of the course. Keep its location private (i.e. do not share the URL with others).
*The WikED toolbar along the top of the page has a number of tools for:
**adding citation references,
**superscript and subscripting (the H2O WikEd symbol will automatically do this for a formula),
**creating tables
**adding links (Wiki links are internal, External links do what they say on the tin)
**# local to the wiki, as <nowiki>[[mod:writeup|text of link]]</nowiki>
**# remote, as <nowiki>[http://www.webelements.com/ text of link]</nowiki>
**# Interwiki, as <nowiki>[[w:Mauveine|Mauveine]]</nowiki>
**# DOI links are invoked using the DOI template <nowiki>{{DOI|..the doi string ..}}</nowiki> or the more modern form <nowiki>[[doi:..the dpi string..]]</nowiki>
**# Links to an Acrobat file you have previously uploaded to the Wiki can be invoked using this template: <nowiki>{{Pdf|tables_for_group_theory.pdf|...description of link ...}}</nowiki>
**# There are lots of other [[Special:UncategorizedTemplates|templates]] to make your life easier such as the [[w:Template:Chembox|ChemBox]]
**If you need some help, invoke it from the left hand side of this page.
*Upload all graphics files also with unique names (so that they do not conflict with other people's names). If you are asked to replace an image, '''REFUSE''' since you are likely to be over-writing someone else's image!
** Invoke such an uploaded file as <nowiki>[[image:nameoffile.jpg|right|200px|Caption]] </nowiki>
**We support WikiComons, whereby images from the [http://commons.wikimedia.org/wiki/Main_Page content (of ~10 million files)] from [http://meta.wikimedia.org/wiki/Wikimedia_Commons Wikimedia Commons Library] can be referenced for your own document. If there is a name conflict, then the local version will be used before the Wiki Commons one.
***To find a file, go to [http://commons.wikimedia.org/wiki/Main_Page Commons]
***Find the file you want using the search facility
***Invoke the top menu, '''use this file in a Wiki''', and copy the string it gives you into your Wiki page
*** <nowiki>[[File:Armstrong Edward centric benzene.jpg|thumb|Armstrong Edward centric benzene]]</nowiki>
*Colour can be added (sparingly) using this {{fontcolor1|yellow|black|text fontcolor}} template. (invoked as <nowiki>{{fontcolor1|yellow|black|text fontcolor}}</nowiki> )
*Save and preview constantly (this makes a new version, which you can always revert to). It goes without saying that you should not reference this page from any other page, or indeed tell anyone else its name.
*'''Important:''' Every 1-2 hours, you might also want to make a [[Mod:writeup#Backing_up_your_report|backup of your report]]. This is particularly important when adding Jmol material, since any error in the pasted code can result in XML errors. The current Wiki version does not flag these errors properly, but instead just hangs the page. Whilst you can try to [[Mod:writeup#Fixing_broken__Pages|repair the page]] as described below, it is much safer to also have a backup!
*You should get into the habit of recording results, and appropriate discussion, soon after they are available, in the manner of a laboratory note book.

== More Editing features ==
=== Handling References/citations with a DOI ===
This section shows how literature citations<ref name="jp027596s">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343. {{DOI|10.1021/ja9825332}}</ref> can be added to text<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref> using the '''<nowiki>{{DOI|value}}</nowiki>''' (digital object identifier) template to produce a nice effect. Citations can be easily added from the WikED toolbar.
*The following text is added to the wiki, exactly as shown here: '''<nowiki><ref name="ja9825332">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343.{{DOI|10.1021/ja9825332}}</ref></nowiki>'''
*Giving a reference a unique identifier, such as '''<nowiki><ref name="ja9825332"></nowiki>''' allows you to refer to the same footnote again by using a ref tag with the same name. The text inside the second tag doesn't matter, because the text already exists in the first reference. You can either copy the whole footnote, or you can use a terminated empty ref tag that looks like this: '''<nowiki><ref name="ja9825332" /></nowiki>'''.
*Collected citations will appear below wherever you place the '''<nowiki><references /></nowiki>''' tag, as here. If you forget to include this tag, the references will not appear!
==== Including the DOI for your experiment data ====
The datasets associated with your experiment can be given a DOI by '''publishing''' any entry in the [https://scanweb.cc.imperial.ac.uk/uportal2/ SCAN Portal]. You can include this DOI as a normal citation.<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref>

==== Additional citation handling ====
* A macro-based reference formatting program has been developed in Microsoft Excel to not only produce the wiki code for direct pasting into your report, but that '''''also''''' formats text for placing in documents, such as synthesis lab reports. This program is available [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Reference_Formatting_Program here].
* A '''[[Template:Cite_journal|Cite journal]] template''' is installed for anyone who wants to experiment
----

References and citations
<references />

----

=== Using an iPad ===

[https://itunes.apple.com/gb/app/wiki-edit/id391012741?mt=8 Wiki Edit] for IOS allows a Wiki to be edited using an iPad. You can dictate your text using '''Siri''' if your speed at '''thumb-typing''' is not what it should be.

= Bringing your report to life =
== Basic JSmol ==
You can use coordinate files created as part of your work (in CML or Molfile format) to insert rotating molecules for your page.
#Using your graphical program (ChemBio3D or Gaussview), '''save''' your molecule as an '''MDL File''', which has the extension '''.mol''', or as '''chemical markup language''', which has the extension '''.cml'''.
#Or, if your calculation ran on the SCAN batch system, '''publish''' the calculation, and in the resulting deposited space, download the .cml or the '''logfile.out''' file to be found there (the latter should be used for vibrations only).
#On the Wiki, '''Upload File''' (from the left hand panel) and select the molecule file you have just placed on your hard drive as above.
#On your Wiki page, insert <nowiki><jmolFile text="Explanatory text for link">BCl3-09.log</jmolFile></nowiki> where in this example, BCl3-09.log is the just uploaded file.
##The should produce <jmolFile text="this link">BCl3-09.log</jmolFile>. When clicked, it will open up a separate floating window for your molecule.
##Further actions upon the loaded molecule (such as selecting a vibrational mode and animating the vibration) are done by right-mouse clicking in the Jmol window.

#When using animations, please let them pop up in a separate window using the <jmolAppletButton> function. Your browser won't slow down and you will make your life so much simpler. =)
##Read more on how to do that [http://wiki.jmol.org/index.php/MediaWiki#Jmol_applet_in_a_popup_window here ]. --[[User:Rea12|Rea12]] 20:58, 8 September 2014 (BST)

== Advanced JSmol ==

A much more powerful invocation is as follows. The following allows a molecule to be directly embedded into the report, and it also shows how to put a script in to control the final display.
{| class="wikitable" border="2"
|-
! copy/paste either of the two sections below into your own Wiki
|-
|<pre><jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>yourmolecule.cml</uploadedFileContents>
</jmolApplet>
</jmol>


<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script><uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol></pre>
|-
! First molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])
|-
|<jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color><size>300</size>
<script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script>
<uploadedFileContents>pentahelicene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Second molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])

|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script>
<uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Every time you embed a molecule in a Wiki page in the above manner, the Web browser must set aside memory. Too many molecules, and the memory starts to run out, and the browser may slow down significantly. So use the feature sparingly, only including key examples where some structural feature would benefit from the rotational capabilities.
It is [http://chemapps.stolaf.edu/jmol/docs/ possible] to add many other commands to the JSmol container above. For example, '''<nowiki><script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script></nowiki>''' will colour atoms 3 4 and 5 (obtained by mouse-overs) purple, and then measure the length of the 3-5 bond. Further examples of how to invoke Jmol are [http://www.mediawiki.org/wiki/Extension:Jmol#Installing_Jmol_Extension found here], and a comprehensive list [http://chemapps.stolaf.edu/jmol/docs/ given here].

== Incorporating orbital/electrostatic potential isosurfaces ==
The procedure is as follows
# Run a Gaussian calculation on the SCAN
# When complete, select ''Formatted checkpoint file'' from the output files and download
# Double click on the file to load into Gaussview
##To generate a molecule orbital, '''Edit/MOs''' and select (= yellow) your required orbitals.
##* '''Visualise''' and '''Update''' to generate them
## To generate an electrostatic potential, '''Results/Surfaces and Contours''', then '''Cube Actions/New Cube/Type=ESP'''. This will take 2-3 minutes to generate
##* In '''Surfaces available''' pre-set the Density to '''0.02''' and then '''Surface Actions/New Surface'''. Try experimenting with the value of Density for the best result. Save the cube as per below.
# In '''Results/Surfaces and contours''' from the '''cubes available''' list, select one and '''Cube actions/save cube'''
# Invoke [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ this page] and you will be asked to select your cube file,
# followed by three file save dialogs, one for the coordinates (.xyz), one for the MO surface (.jvxl) and a shrink-wrapped bundle (.pngj).
# Insert the following code into your Wiki, replacing the file name with your own choice from the preceding file save dialogs.
<pre><nowiki><jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol></nowiki>
</pre>
# [[image:absolute_path.jpg|right|350px]]Next, upload these two files into the Wiki (one file at a time, the multiple file uploader does not seem to work for this task)
## Now for the tough bit. You will need to find the absolute path for the .jvxl file. Above, this appears as images/1/1b/AHB_mo22-2.cub.jvxl
## Just after uploading a .jvxl file, you will see a response as shown on the right.
## Right click on '''Edit this file using an external application'''. You can used any text editor (Wordpad etc).
## This text file will contain something like: <tt>; or go to the URL <nowiki>https://wiki.ch.ic.ac.uk/wiki/images/1/1b/AHB_mo22-2.cub.jvxl</nowiki></tt>
#Select just the string '''images/1/1b/AHB_mo22-2.cub.jvxl''' and paste it in as shown above:
#You should get something akin to:
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;
</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
* You can superimpose two surfaces. Change the script contents above to append a second surface to the first: <pre><script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;isosurface append color red blue "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script></pre>
* The four colours used in this line can be changed to whatever you consider appropriate.
=== An alternative way of loading surfaces ===
This method avoids the need to specify paths to files as seen above. Instead uses the '''.pngj''' bundle which contains all necessary information and can be invoked by
<pre><nowiki><jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile></nowiki></pre> which produces <jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile>.
# It only supports one surface (you cannot superimpose two orbitals)
# You can also load other surfaces, such as <jmolFile text="molecular electrostatic potentials">Checkpoint_60018_esp.cub.pngj‎</jmolFile> generated from a cube of electrostatic potential (ESP) values created using Gaussview as follows:
## Download .fchk file from SCAN
## Open using Gaussview
## '''Results/Surfaces & contours/Cube actions/New Cube/ESP''' and then '''cube actions/save cube''' which is how the above was generated. You may have to play around with the value of the density (~0.02).

=== MOPAC orbitals ===
# Run MOPAC from ChemBio3D, selecting '''Compute Properties/Molecular Surface''' from the '''properties''' pane, and in the '''General pane''' specify a location for the output and deselect '''Kill temporary files''' if not already so.
# Upload the '''.mgf''' file so produced to the Wiki
# Invoke as follows ('''MO 35;''' means the 35th most stable orbital for that molecule).
<pre><nowiki><jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>300</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol></nowiki></pre>
<jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>200</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol>

== Enhancing your report with Equations ==
*You may have need to express some [http://meta.wikimedia.org/wiki/Help:Formula equations] on the Wiki. This is currently supported only using a notation derived from '''LaTeX''', and as with the Jmol insertion above, is enabled within a '''<nowiki><math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math></nowiki>''' field inserted using the default editor (the SQRT(n) button), and producing the following effect:
<math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math>

The requisite syntax can be produced by using
*MathType as an equation editor (used standalone or in Word). It places the required LaTeX onto the clipboard for pasting into the Wiki).
*[http://www.lyx.org/ Lyx] which is a free stand-alone editor.
*A more general solution to this problem is simply to create a graphical image of your equation, and insert that instead as a picture.

== Inserting Tables ==
Instead of inserting screenshots of Excel, tables can be produced using MediaWiki markup (see [http://www.mediawiki.org/wiki/Help:Tables this page]), where you can also find lots of examples of different styles of table. However, this can be quite time consuming when you have a lot of tabulated data and need to copy it from somewhere like Excel into ChemWiki. Instead of typing it by hand, you can save your Excel worksheet as a comma separated file (.csv) and then use this [[http://area23.brightbyte.de/csv2wp.php CSV to MediaWiki markup]] convertor. Note that cells starting with "-", e.g. for negative numbers, need a space inserted between the - and | in the output otherwise MediaWiki interprets it as a new row.

Another web-based utility is available called [http://excel2wiki.net/ Excel2Wiki] which can be used to generate MediaWiki code from an Excel table.

== SVG (for display of IR/NMR/Chiroptical Spectra) ==
[[File:IR.svg|300px|right|SVG]]SVG stands for '''scaleable-vector-graphics'''. Its advantage is well, that it scales properly (but it has many others, including the ability to make simple edit to captions etc using Wordpad or similar). From your point of view, it is readily generated using Gaussview. If you view an '''IR/NMR/UV-vis/IRC/Scan/''' spectrum in this program, it allows you to export the spectrum as SVG (right-mouse-click on the spectrum to pull down the required menu). Upload this file, and invoke it as <nowiki>[[File:IR.svg|200px|right|SVG]]</nowiki> If you open eg IR.svg in Wordpad (or other text editor), you can edit the captions, font sizes etc (its fairly obvious). Oh, you will need to use a web browser that actually displays SVG. Internet Explorer 8 does not (9 is supposed to). Use Firefox/Chrome/Safari etc.

== Chemical Templates ==
An example is the [[w:Template:Chembox|ChemBox]]. Volunteers needed to test/extend these!

= Submitting your report =


--[[User:Mjbear|Mjbear]] ([[User talk:Mjbear|talk]]) 22:24, 22 October 2015 (BST)
For the '''Computational Chemistry Lab''': submit your wiki URL address on Blackboard by 12:00 on the friday of the 2-week experiment.
The link is here: https://bb.imperial.ac.uk/webapps/blackboard/content/listContentEditable.jsp?content_id=_705671_1&course_id=_8223_1&content_id=_705733_1

= Backing up your report =
[[Image:export1.jpg|left|250px]][[Image:Export2.jpg|right|200px]]Invoke [[Special:Export|this utility]] to back your project up. In the box provided, enter e.g. '''Mod:wzyz1234''' being the password for your report. This will generate a page (right) which can be saved using the Firefox '''File/Save_Page_as''' menu. Specify '''Web Page, XML only''' as the format, and add .xml to the file suffix. You might want to do this eg on a daily basis to secure against corruption. This is in addition to the notes for how to repair broken pages.

The same file can now be reloaded using [[Special:Import|Import]].

= Fixing broken Pages =
There are several ways in which a page can break.

*We have had instances of people inserting a corrupted version of the Jmol lines into their project, resulting in a '''XML error''' or '''Database error'''. Recovering from such an error is not simple. So we do ask that you carefully check what you are pasting into the Wiki, and that its form is exactly as shown above. For example, below is a real example of inducing such an error. Can you see where the fault lies? (Answer: the <nowiki><jmol></nowiki> tag is not matched by <nowiki></jmol></nowiki>. If tags are not balanced, XML errors will occur).
<pre><jmol><jmolApplet><title>equatorial</title><color>white</color>
<size>200</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Pl506_14_equatorial.mol</uploadedFileContents></pre>
*Another example might be wish to indicate a citation using <nowiki><ref>...details </ref></nowiki> but in fact end up entering <nowiki><ref> ...</nowiki> (i.e. missing out the <nowiki></ref></nowiki>)
*If you do encounter such an error, try invoking your project as '''<nowiki>https://www.ch.ic.ac.uk/wiki/index.php?title=Mod:wzyz1234&action=history</nowiki>''' and edit and then save an uncorrupted version. You will need to be already logged in before you attempt to view the history in this way, since logging in '''after''' you invoke the above will return you not to the history, but to the corrupted page (Hint: it sometimes helps to check '''Remember my login on this computer''' as you log in). For example, the history for this page can be seen [https://www.ch.imperial.ac.uk/wiki/index.php?title=Mod:writeup&action=history here]. You can eg load this preceeding page, and then use it to replace '''writeup''' with your own project address.
*If the preceeding does not work try the instructions shown [[mod:fix|here]].

= Feedback =
Each Wiki page has a discussion section, including your submitted report page. 

See also: [[Mod:Cheatsheet|cheatsheet]]

Mod:writeup

2015-10-22T21:24:03Z

Mjbear: /* Submitting your report */

See also: [[Mod:Cheatsheet|Cheatsheet]].

== The expected length of the report ==
A Wiki does not have pages as such. But as a very rough guide, expect to produce something the equivalent of about six printed pages (although you can invoke ''pop-ups'' and the like which make a page count only very approximate). Use graphics reasonably sparingly, and to the point.

= Why Wiki? =
Since everyone is used to using [http://www.wordonwiki.com Microsoft Word], why do we [[talks:rzepa2011|use a Wiki]] for this course? Well, the Wiki format has several advantages.
#A full revision and fully dated history across sessions is kept (Word only keeps this during a session). This is more suited for laboratory work, where you indeed might need to go back to a particular day and experiment to check your notes.
#The (chemistry) Wiki allows you to include molecule coordinates, vibrations and MO surfaces which can be rotated and inspected, along with other chemical extensions. Word does not offer this.
#The Wiki allows you to include "zoomable" graphics in the form of SVG (which Gaussview generates), and access to the 17-million large [http://commons.wikimedia.org/wiki/Main_Page WikiCommons] image library, as well as access to the Wikipedia InterWiki.
#The [[w::Help:Template|template]] concept allows pre-formated entry. There are lots of powerful [[w:Category:Chemical_element_symbol_templates|chemical templates]] available.
#Autonumbered referencing, and particularly cross-referencing, is actually easier than using Word.
#You (and the graders) can access your report anywhere online, it is not held on a local hard drive which you may not have immediate access to.
#It has automatic date and identity stamps for ALL components, which means we can assess that part of the report handed in by any deadline, and deal separately with anything which has a date-stamp past a given deadline. A Word document has only a single date-and-time stamp and so deadlines must apply to the whole document.
#And we have been using Wikis for course work since '''2006''', so there is lots of expertise around!
#And finally, Wiki is an example of a [http://en.wikipedia.org/wiki/Markdown MarkDown] language, one designed to facilitate writing using an easy-to-read, easy-to-write plain text format (with the option of converting it to structurally valid XHTML).

=Report Preparation =

== Before you start writing ==
Before you start writing, you might wish to read this article<ref name="adma.200400767">G.M. Whitesides, "Whitesides' Group: Writing a Paper", ''Advanced Materials'', '''2004''', ''16'', 1375–137 {{DOI|10.1002/adma.200400767}}</ref> (or perchance this advice<ref name="ac2000169">R. Murray, "Skillful writing of an awful research paper", ''Anal. Chem.'', '''2011''', ''83'', 633. {{DOI|10.1021/ac2000169}}</ref>). In your report you should discuss your evaluation of each of the techniques you use here. You should include at least '''three literature references in addition to the ones given here'''. You might also want to check the [[Mod:latebreak|late breaking news]] to see if there are any helpful hints about the project you might want to refer to. You will be writing your report in Wiki format, and it is best to do this continually as you do the experiment. In effect, your Wiki report is also your laboratory manual.

#[[File:Wiked.jpg|right|400px|WikED editor]]Open Firefox as a Web browser.
#There should be a tab for the course Wiki, but if not, use the URL '''www.ch.ic.ac.uk'''
#*[[Image:exception1.jpg|right|thumb|Security exception]]If the browser asks you to add a security exception, do so and proceed to '''view/confirm''' the certificate.
#You can view the Wiki without logging in, but to create a report, you will have to login as yourself. Check '''Remember my login on this computer'''
#Before you start, you might want to visit the [[Special:Preferences|preferences]] page to customise the Wiki for yourself.
#Follow the procedures below. Check that the WikED icon is present at the top, just to the right of the log out text (ringed in red). If you want a minimalist editing interface, click this icon to switch it off. A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.

=== Assigning your report an identifier ===
#*[[Image:New_report.jpg|right|400px|Creating a report page]] In the address box, type something like
#**'''wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:{{fontcolor1|yellow|black|XYZ1234}}'''
#*The characters '''Mod''' indicate a report associated with the modelling course, and '''{{fontcolor1|yellow|black|XYZ1234}}''' is your secret password for the report. It can be any length, but do not make it too long! It should then tell you there is no text in this page. If not, try another more unique password. You should now click on the '''edit this page''' link to start. Use a different address for each module of the course you are submitting.
#*It is a {{fontcolor1|yellow|black|good idea}} to add a bookmark to this page, so that you can go back to it quickly.
==== Assigning your report a persistent (DOI-style) identifier.====
Use [http://spectradspace.lib.imperial.ac.uk/url2handle/ this tool] to assign a shorter identifier for your report (one that can be invoked using eg <nowiki>{{DOI|shortidentifier]]</nowiki>.

=== Converters to the Wiki format ===
#Convert a Word document. Open it in '''OpenOffice''' (rather than the Microsoft version) and '''export''' as Mediawiki. Open the resulting .txt file in eg WordPad, select all the text, copy, and then paste this into the Wiki editing page. You will still have to upload the graphical images from the original Word document separately.
#There is also a [http://labs.seapine.com/htmltowiki.cgi HTML to Wiki] converter which you can use to import HTML code from an existing Web page into a (Media)Wiki.

== Basic editing ==
An [[Mod:inorganic_wiki_page_instructions|introductory tutorial]] is available which complements the information here.
*A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.
*[[Image:report12345.jpg|right|thumb|The editing environment]]You will need to create a separate report page on this Wiki for each module of the course. Keep its location private (i.e. do not share the URL with others).
*The WikED toolbar along the top of the page has a number of tools for:
**adding citation references,
**superscript and subscripting (the H2O WikEd symbol will automatically do this for a formula),
**creating tables
**adding links (Wiki links are internal, External links do what they say on the tin)
**# local to the wiki, as <nowiki>[[mod:writeup|text of link]]</nowiki>
**# remote, as <nowiki>[http://www.webelements.com/ text of link]</nowiki>
**# Interwiki, as <nowiki>[[w:Mauveine|Mauveine]]</nowiki>
**# DOI links are invoked using the DOI template <nowiki>{{DOI|..the doi string ..}}</nowiki> or the more modern form <nowiki>[[doi:..the dpi string..]]</nowiki>
**# Links to an Acrobat file you have previously uploaded to the Wiki can be invoked using this template: <nowiki>{{Pdf|tables_for_group_theory.pdf|...description of link ...}}</nowiki>
**# There are lots of other [[Special:UncategorizedTemplates|templates]] to make your life easier such as the [[w:Template:Chembox|ChemBox]]
**If you need some help, invoke it from the left hand side of this page.
*Upload all graphics files also with unique names (so that they do not conflict with other people's names). If you are asked to replace an image, '''REFUSE''' since you are likely to be over-writing someone else's image!
** Invoke such an uploaded file as <nowiki>[[image:nameoffile.jpg|right|200px|Caption]] </nowiki>
**We support WikiComons, whereby images from the [http://commons.wikimedia.org/wiki/Main_Page content (of ~10 million files)] from [http://meta.wikimedia.org/wiki/Wikimedia_Commons Wikimedia Commons Library] can be referenced for your own document. If there is a name conflict, then the local version will be used before the Wiki Commons one.
***To find a file, go to [http://commons.wikimedia.org/wiki/Main_Page Commons]
***Find the file you want using the search facility
***Invoke the top menu, '''use this file in a Wiki''', and copy the string it gives you into your Wiki page
*** <nowiki>[[File:Armstrong Edward centric benzene.jpg|thumb|Armstrong Edward centric benzene]]</nowiki>
*Colour can be added (sparingly) using this {{fontcolor1|yellow|black|text fontcolor}} template. (invoked as <nowiki>{{fontcolor1|yellow|black|text fontcolor}}</nowiki> )
*Save and preview constantly (this makes a new version, which you can always revert to). It goes without saying that you should not reference this page from any other page, or indeed tell anyone else its name.
*'''Important:''' Every 1-2 hours, you might also want to make a [[Mod:writeup#Backing_up_your_report|backup of your report]]. This is particularly important when adding Jmol material, since any error in the pasted code can result in XML errors. The current Wiki version does not flag these errors properly, but instead just hangs the page. Whilst you can try to [[Mod:writeup#Fixing_broken__Pages|repair the page]] as described below, it is much safer to also have a backup!
*You should get into the habit of recording results, and appropriate discussion, soon after they are available, in the manner of a laboratory note book.

== More Editing features ==
=== Handling References/citations with a DOI ===
This section shows how literature citations<ref name="jp027596s">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343. {{DOI|10.1021/ja9825332}}</ref> can be added to text<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref> using the '''<nowiki>{{DOI|value}}</nowiki>''' (digital object identifier) template to produce a nice effect. Citations can be easily added from the WikED toolbar.
*The following text is added to the wiki, exactly as shown here: '''<nowiki><ref name="ja9825332">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343.{{DOI|10.1021/ja9825332}}</ref></nowiki>'''
*Giving a reference a unique identifier, such as '''<nowiki><ref name="ja9825332"></nowiki>''' allows you to refer to the same footnote again by using a ref tag with the same name. The text inside the second tag doesn't matter, because the text already exists in the first reference. You can either copy the whole footnote, or you can use a terminated empty ref tag that looks like this: '''<nowiki><ref name="ja9825332" /></nowiki>'''.
*Collected citations will appear below wherever you place the '''<nowiki><references /></nowiki>''' tag, as here. If you forget to include this tag, the references will not appear!
==== Including the DOI for your experiment data ====
The datasets associated with your experiment can be given a DOI by '''publishing''' any entry in the [https://scanweb.cc.imperial.ac.uk/uportal2/ SCAN Portal]. You can include this DOI as a normal citation.<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref>

==== Additional citation handling ====
* A macro-based reference formatting program has been developed in Microsoft Excel to not only produce the wiki code for direct pasting into your report, but that '''''also''''' formats text for placing in documents, such as synthesis lab reports. This program is available [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Reference_Formatting_Program here].
* A '''[[Template:Cite_journal|Cite journal]] template''' is installed for anyone who wants to experiment
----

References and citations
<references />

----

=== Using an iPad ===

[https://itunes.apple.com/gb/app/wiki-edit/id391012741?mt=8 Wiki Edit] for IOS allows a Wiki to be edited using an iPad. You can dictate your text using '''Siri''' if your speed at '''thumb-typing''' is not what it should be.

= Bringing your report to life =
== Basic JSmol ==
You can use coordinate files created as part of your work (in CML or Molfile format) to insert rotating molecules for your page.
#Using your graphical program (ChemBio3D or Gaussview), '''save''' your molecule as an '''MDL File''', which has the extension '''.mol''', or as '''chemical markup language''', which has the extension '''.cml'''.
#Or, if your calculation ran on the SCAN batch system, '''publish''' the calculation, and in the resulting deposited space, download the .cml or the '''logfile.out''' file to be found there (the latter should be used for vibrations only).
#On the Wiki, '''Upload File''' (from the left hand panel) and select the molecule file you have just placed on your hard drive as above.
#On your Wiki page, insert <nowiki><jmolFile text="Explanatory text for link">BCl3-09.log</jmolFile></nowiki> where in this example, BCl3-09.log is the just uploaded file.
##The should produce <jmolFile text="this link">BCl3-09.log</jmolFile>. When clicked, it will open up a separate floating window for your molecule.
##Further actions upon the loaded molecule (such as selecting a vibrational mode and animating the vibration) are done by right-mouse clicking in the Jmol window.

#When using animations, please let them pop up in a separate window using the <jmolAppletButton> function. Your browser won't slow down and you will make your life so much simpler. =)
##Read more on how to do that [http://wiki.jmol.org/index.php/MediaWiki#Jmol_applet_in_a_popup_window here ]. --[[User:Rea12|Rea12]] 20:58, 8 September 2014 (BST)

== Advanced JSmol ==

A much more powerful invocation is as follows. The following allows a molecule to be directly embedded into the report, and it also shows how to put a script in to control the final display.
{| class="wikitable" border="2"
|-
! copy/paste either of the two sections below into your own Wiki
|-
|<pre><jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>yourmolecule.cml</uploadedFileContents>
</jmolApplet>
</jmol>


<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script><uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol></pre>
|-
! First molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])
|-
|<jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color><size>300</size>
<script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script>
<uploadedFileContents>pentahelicene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Second molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])

|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script>
<uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Every time you embed a molecule in a Wiki page in the above manner, the Web browser must set aside memory. Too many molecules, and the memory starts to run out, and the browser may slow down significantly. So use the feature sparingly, only including key examples where some structural feature would benefit from the rotational capabilities.
It is [http://chemapps.stolaf.edu/jmol/docs/ possible] to add many other commands to the JSmol container above. For example, '''<nowiki><script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script></nowiki>''' will colour atoms 3 4 and 5 (obtained by mouse-overs) purple, and then measure the length of the 3-5 bond. Further examples of how to invoke Jmol are [http://www.mediawiki.org/wiki/Extension:Jmol#Installing_Jmol_Extension found here], and a comprehensive list [http://chemapps.stolaf.edu/jmol/docs/ given here].

== Incorporating orbital/electrostatic potential isosurfaces ==
The procedure is as follows
# Run a Gaussian calculation on the SCAN
# When complete, select ''Formatted checkpoint file'' from the output files and download
# Double click on the file to load into Gaussview
##To generate a molecule orbital, '''Edit/MOs''' and select (= yellow) your required orbitals.
##* '''Visualise''' and '''Update''' to generate them
## To generate an electrostatic potential, '''Results/Surfaces and Contours''', then '''Cube Actions/New Cube/Type=ESP'''. This will take 2-3 minutes to generate
##* In '''Surfaces available''' pre-set the Density to '''0.02''' and then '''Surface Actions/New Surface'''. Try experimenting with the value of Density for the best result. Save the cube as per below.
# In '''Results/Surfaces and contours''' from the '''cubes available''' list, select one and '''Cube actions/save cube'''
# Invoke [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ this page] and you will be asked to select your cube file,
# followed by three file save dialogs, one for the coordinates (.xyz), one for the MO surface (.jvxl) and a shrink-wrapped bundle (.pngj).
# Insert the following code into your Wiki, replacing the file name with your own choice from the preceding file save dialogs.
<pre><nowiki><jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol></nowiki>
</pre>
# [[image:absolute_path.jpg|right|350px]]Next, upload these two files into the Wiki (one file at a time, the multiple file uploader does not seem to work for this task)
## Now for the tough bit. You will need to find the absolute path for the .jvxl file. Above, this appears as images/1/1b/AHB_mo22-2.cub.jvxl
## Just after uploading a .jvxl file, you will see a response as shown on the right.
## Right click on '''Edit this file using an external application'''. You can used any text editor (Wordpad etc).
## This text file will contain something like: <tt>; or go to the URL <nowiki>https://wiki.ch.ic.ac.uk/wiki/images/1/1b/AHB_mo22-2.cub.jvxl</nowiki></tt>
#Select just the string '''images/1/1b/AHB_mo22-2.cub.jvxl''' and paste it in as shown above:
#You should get something akin to:
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;
</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
* You can superimpose two surfaces. Change the script contents above to append a second surface to the first: <pre><script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;isosurface append color red blue "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script></pre>
* The four colours used in this line can be changed to whatever you consider appropriate.
=== An alternative way of loading surfaces ===
This method avoids the need to specify paths to files as seen above. Instead uses the '''.pngj''' bundle which contains all necessary information and can be invoked by
<pre><nowiki><jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile></nowiki></pre> which produces <jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile>.
# It only supports one surface (you cannot superimpose two orbitals)
# You can also load other surfaces, such as <jmolFile text="molecular electrostatic potentials">Checkpoint_60018_esp.cub.pngj‎</jmolFile> generated from a cube of electrostatic potential (ESP) values created using Gaussview as follows:
## Download .fchk file from SCAN
## Open using Gaussview
## '''Results/Surfaces & contours/Cube actions/New Cube/ESP''' and then '''cube actions/save cube''' which is how the above was generated. You may have to play around with the value of the density (~0.02).

=== MOPAC orbitals ===
# Run MOPAC from ChemBio3D, selecting '''Compute Properties/Molecular Surface''' from the '''properties''' pane, and in the '''General pane''' specify a location for the output and deselect '''Kill temporary files''' if not already so.
# Upload the '''.mgf''' file so produced to the Wiki
# Invoke as follows ('''MO 35;''' means the 35th most stable orbital for that molecule).
<pre><nowiki><jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>300</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol></nowiki></pre>
<jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>200</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol>

== Enhancing your report with Equations ==
*You may have need to express some [http://meta.wikimedia.org/wiki/Help:Formula equations] on the Wiki. This is currently supported only using a notation derived from '''LaTeX''', and as with the Jmol insertion above, is enabled within a '''<nowiki><math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math></nowiki>''' field inserted using the default editor (the SQRT(n) button), and producing the following effect:
<math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math>

The requisite syntax can be produced by using
*MathType as an equation editor (used standalone or in Word). It places the required LaTeX onto the clipboard for pasting into the Wiki).
*[http://www.lyx.org/ Lyx] which is a free stand-alone editor.
*A more general solution to this problem is simply to create a graphical image of your equation, and insert that instead as a picture.

== Inserting Tables ==
Instead of inserting screenshots of Excel, tables can be produced using MediaWiki markup (see [http://www.mediawiki.org/wiki/Help:Tables this page]), where you can also find lots of examples of different styles of table. However, this can be quite time consuming when you have a lot of tabulated data and need to copy it from somewhere like Excel into ChemWiki. Instead of typing it by hand, you can save your Excel worksheet as a comma separated file (.csv) and then use this [[http://area23.brightbyte.de/csv2wp.php CSV to MediaWiki markup]] convertor. Note that cells starting with "-", e.g. for negative numbers, need a space inserted between the - and | in the output otherwise MediaWiki interprets it as a new row.

Another web-based utility is available called [http://excel2wiki.net/ Excel2Wiki] which can be used to generate MediaWiki code from an Excel table.

== SVG (for display of IR/NMR/Chiroptical Spectra) ==
[[File:IR.svg|300px|right|SVG]]SVG stands for '''scaleable-vector-graphics'''. Its advantage is well, that it scales properly (but it has many others, including the ability to make simple edit to captions etc using Wordpad or similar). From your point of view, it is readily generated using Gaussview. If you view an '''IR/NMR/UV-vis/IRC/Scan/''' spectrum in this program, it allows you to export the spectrum as SVG (right-mouse-click on the spectrum to pull down the required menu). Upload this file, and invoke it as <nowiki>[[File:IR.svg|200px|right|SVG]]</nowiki> If you open eg IR.svg in Wordpad (or other text editor), you can edit the captions, font sizes etc (its fairly obvious). Oh, you will need to use a web browser that actually displays SVG. Internet Explorer 8 does not (9 is supposed to). Use Firefox/Chrome/Safari etc.

== Chemical Templates ==
An example is the [[w:Template:Chembox|ChemBox]]. Volunteers needed to test/extend these!

= Submitting your report =


For the '''Computational Chemistry Lab''': submit your wiki URL address on Blackboard by 12:00 on the friday of the 2-week experiment.
The link is here: https://bb.imperial.ac.uk/webapps/blackboard/content/listContentEditable.jsp?content_id=_705671_1&course_id=_8223_1&content_id=_705733_1

= Backing up your report =
[[Image:export1.jpg|left|250px]][[Image:Export2.jpg|right|200px]]Invoke [[Special:Export|this utility]] to back your project up. In the box provided, enter e.g. '''Mod:wzyz1234''' being the password for your report. This will generate a page (right) which can be saved using the Firefox '''File/Save_Page_as''' menu. Specify '''Web Page, XML only''' as the format, and add .xml to the file suffix. You might want to do this eg on a daily basis to secure against corruption. This is in addition to the notes for how to repair broken pages.

The same file can now be reloaded using [[Special:Import|Import]].

= Fixing broken Pages =
There are several ways in which a page can break.

*We have had instances of people inserting a corrupted version of the Jmol lines into their project, resulting in a '''XML error''' or '''Database error'''. Recovering from such an error is not simple. So we do ask that you carefully check what you are pasting into the Wiki, and that its form is exactly as shown above. For example, below is a real example of inducing such an error. Can you see where the fault lies? (Answer: the <nowiki><jmol></nowiki> tag is not matched by <nowiki></jmol></nowiki>. If tags are not balanced, XML errors will occur).
<pre><jmol><jmolApplet><title>equatorial</title><color>white</color>
<size>200</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Pl506_14_equatorial.mol</uploadedFileContents></pre>
*Another example might be wish to indicate a citation using <nowiki><ref>...details </ref></nowiki> but in fact end up entering <nowiki><ref> ...</nowiki> (i.e. missing out the <nowiki></ref></nowiki>)
*If you do encounter such an error, try invoking your project as '''<nowiki>https://www.ch.ic.ac.uk/wiki/index.php?title=Mod:wzyz1234&action=history</nowiki>''' and edit and then save an uncorrupted version. You will need to be already logged in before you attempt to view the history in this way, since logging in '''after''' you invoke the above will return you not to the history, but to the corrupted page (Hint: it sometimes helps to check '''Remember my login on this computer''' as you log in). For example, the history for this page can be seen [https://www.ch.imperial.ac.uk/wiki/index.php?title=Mod:writeup&action=history here]. You can eg load this preceeding page, and then use it to replace '''writeup''' with your own project address.
*If the preceeding does not work try the instructions shown [[mod:fix|here]].

= Feedback =
Each Wiki page has a discussion section, including your submitted report page. 

See also: [[Mod:Cheatsheet|cheatsheet]]

Mod:intro

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Mjbear:

See also: [[http://wiki.ch.ic.ac.uk/wiki/index.php?title=Main_Page#Third_Year_Computational_Chemistry_Lab|Comp Chem Lab]],  [[Mod:writeup|Writing up]]



== Specific times ==

*Week 2 (Friday): '''submit the wiki address for your report on Blackboard by 12:00'''
**You can submit your wiki address early (before 12:00) and continue to edit your wiki up to 12:00.
**Any material added after 12:00 will not be marked (unless you have been granted an extension)

== Locations ==
Work in the computer lab on Level 2 (232A). 


== Expected hours in the Lab ==

The lab times are 14:00-17:00 on Mon, Tue, Thur and Fri. You not restricted to these times, but you should be able to complete your computational experiment over two weeks and write up in the time available. It is up to you to manage your time: do not do too much or too little. Ask a demonstrator or staff if you are at all unsure.


No student is expected to spend more time on an individual computational experiment than they would on an experiment in any 3rd year lab based course.


Address your questions to the demonstrators during the lab hours they are available. Some will be contactable via email. If you are struggling with the suggested times allocated for each part of the experiment, seek help from a demonstrator.

== Demonstrator and Staff help and feedback times ==
'''Demonstrators are available Mon, Tue, Thur and Fri in the upstairs / Level 2 computer room, usually from 14:00 to 15:00.'''

If you have a question, talk with a demonstrator first. Demonstrators are not just there to help with specific technical questions, they can also offer '''feedback''' on completed work before it is marked.




== Report submission ==

Submit the URL for your Wiki report from [https://bb.imperial.ac.uk/webapps/blackboard/content/listContentEditable.jsp?content_id=_266665_1&course_id=_1962_1&mode=quick&content_id=_308976_1 this address] by the deadline. These deadlines are on the Friday of the end of the second week of each experiment.

You should expect to get a grade on blackboard within 10 working days. If you have heard nothing and have not received a grade in blackboard, please contact the staff responsible for the experiment to make sure your work has not gone missing.

'''Please note the College policy: work submitted late will receive zero marks.''' Any sections completed by the hand-in date will be assessed for full marks, additional material added after this will not be marked. If you are having problems, are ill or have extenuating circumstances please see [mailto:laura.patel@imperial.ac.uk Dr Patel] as early as possible, extensions may be granted and will be determined on a case-by-case basis.



----

See also:[[http://wiki.ch.ic.ac.uk/wiki/index.php?title=Main_Page#Third_Year_Computational_Chemistry_Lab|Comp Chem Lab]]  [[Mod:writeup|Writing up]]

Main Page

2015-10-09T11:03:23Z

Mjbear: /* Third Year Computational Chemistry Lab */

[[Image:QR_complab.png|right|QR]]
= {{fontcolor1|yellow|black|Chemistry}}{{fontcolor1|orange|black|@}}{{fontcolor1|purple|white|www.ch.imperial.ac.uk}} =
This is a communal area for documenting teaching and laboratory courses. To [[admin:add|add to any content on these pages]], you will have to log in using your Imperial College account.
== ChemDraw/Chemdoodle Hints ==
#[[IT:chemdraw|Useful hints for using ChemDraw/ChemDoodle]]

== Student wiki ==
#[[StudentWiki:Contents|Student pages]]

== Tablet Project ==
# [[tablet:tablet|Tablet Pilot Project]]
== 3D ==
# [[mod:3D|3D-printable models]]
# [[mod:stereo|Lecture Theatre Stereo]]

= Laboratories and Workshops =
== First Year ==
=== [[it:it_facillities|Email and IT@www.ch.imperial.ac.uk]]: A summary of available IT resources ===

===First Year Chemical Information Lab 2014 ===
*[[it:intro-2011|Introduction]]
*[[it:lectures-2011|Lectures]]
*[[it:coursework-2011|Coursework]]
*[[it:assignment-2011|Assignment for the course]]
*[[it:software-2011|List of software for CIT]]
*[[it:searches-2011|Search facilities for CIT]]
*[[Measurement_Science_Lab:_Introduction|Measurement Science Lab Course]]

===[[organic:conventions|Conventions in organic chemistry]]===
===[[organic:arrow|Reactive Intermediates in organic chemistry]]===
===[[organic:stereo|Stereochemical models]] ===

== Second Year ==
===Second Year Modelling Workshop ===
*[[Coursework]]
*[[Second Year Modelling Workshop|Instructions]] and [[mod:further_coursework|Further optional coursework]]
*[[it:conquest|Conquest searches]]




=== Molecular Dynamics (Physical Chemistry Laboratory) ===
*[[Running MD code in MATLAB|Running MD code in MATLAB]]

== Third Year ==

===Third Year Computational Chemistry Lab ===
*[[mod:intro|Information needed for the course]]


*[[mod:writeup|Report writing and submission]]

*[[mod:latebreak|Late breaking news]]
*The course modules

**[[Mod:phys3|Transition states and reactivity.]]
**[[ThirdYearMgOExpt-1415|MgO experiment]]
** [[Third_year_CMP_compulsory_experiment|CMP compulsory experiment: Programming for liquid simulation]]
** [[Third_year_simulation_experiment|Simulation of a simple liquid]]
*[[mod:programs|General program instructions:]]
**[[mod:gaussview|The Gaussview/Gaussian suite]]
**[[Mod:scan|Submitting jobs to the chemistry high-performance-computing resource]]

= Online materials for mobile devices =
# [[ebooks:howto|How to get eBooks]]
# [https://play.google.com/store/apps/details?id=com.blackboard.android&hl=en Blackboard mobile learn for Android]
# [https://itunes.apple.com/us/app/blackboard-mobile-learn/id376413870?mt=8 Blackboard mobile learn for iOS]
# [https://itunes.apple.com/gb/course/id562191620 Pericylic reactions in iTunesU ] (download [https://itunes.apple.com/gb/app/itunes-u/id490217893?mt=8 App] first)
# [https://itunes.apple.com/gb/course/id562191825 Conformational analysis in iTunesU] (download [https://itunes.apple.com/gb/app/itunes-u/id490217893?mt=8 App] first)
# [https://itunes.apple.com/gb/course/id562191342 A library of mechanistic animations in iTunesU] (download [https://itunes.apple.com/gb/app/itunes-u/id490217893?mt=8 App] first)
# [[IT:panopto|How to compress and disseminate Panopto lecture recordings]]
= Material from previous years =
== First year ==
===Introduction to Chemical Programming Workshop 2013===
*[[1da-workshops-2013-14|Workshop script]]


= PG =

# [[rdm:intro|Data management]]

Mod:scan

2015-10-07T16:56:35Z

Mjbear:

===Submitting calculations to the Departmental HPC Cluster ===

[[Image:export.jpg|thumb|right|Export from Ghemical]]The Chemistry department has access to a HPC (high performance computing) system which can be used to run more time consuming calculations than is possible ''interactively'' on a single computer whilst sitting in front of it.

One far more reliable and quantitative way of modelling a molecule is to subject it to quantum mechanical modelling using '''Density Functional''' theory. In practice, this is implemented here using a program called Gaussian 09. The procedure to submit such a job is as follows:
====Creating an Input file ====

*After you have optimised your sketched molecule using Avogadro or Gaussview, as described previously, you will have a Gaussian input file saved in your '''H:''' drive by default.
*[[Image:pentahelicene.jpg|thumb|right|Typical Gaussian input]] The file will have to be edited before it can be submitted. You can do this either with '''Gaussview''' as the program, but a much simpler method is to open the file (''pentahelicene.gjf'' in this example) using eg the Windows Notepad++ editor. Remove any existing lines starting with % or # and replace them with one of the following single lines (the second example also results in the vibrational frequences and from these the entropy being computed, and hence the zero-point and free-energy corrected value, ΔG). This latter option will take significantly longer however. 
<tt># B3LYP/6-31G(d) opt</tt> 
or 
<tt># B3LYP/6-31G(d) opt freq</tt> 
to produce a file that looks like the one shown on the right.
*For a molecule the size of e.g. pentahelicene, the calculation will take about 4-5 hours overnight. If for some reason, your molecule is taking longer, you can always reduce the size of the [[basis set]] to e.g. ''B3LYP/3-21G*'', or submit the job on a Friday, when it will have the entire weekend available to it. If you want greater accuracy (but for longer computing time), try e.g. <tt># B3LYP/cc-pVTZ opt freq</tt>.

====Submitting the Input file ====
*[[Image:scan1.jpg|thumb|right|Create a new job]][https://portal.hpc.imperial.ac.uk/ You will have to login as yourself]. You can submit as many jobs as you wish through this mechanism, but you must prepare an input file for each first (.gjf if you want to run Gaussian).
*[[Image:scan2.jpg|thumb|left|Create a project]][[Image:scan3.jpg|thumb|left|Select a pool]]After you are logged in you should organise your jobs by '''project'''. Create a suitable new project, then select '''New job'''. 
*#'''Compchem Lab 1''' runs continuously during the day and night, has a concurrency of 8 and a time limit of 48 hours.
*Next, select an Application. Two types of Gaussian can be selected: '''Gaussian 4px ''' and '''Gaussian 8px '''
*Next select the Project you have just created, and press '''Continue'''.
*[[Image:scan5.jpg|thumb|left|Upload your input file]]You now have to find the Gaussian input file, as prepared above. You should '''Browse''' to drive H: to find this file. Add a description which will help you identify the job.
*[[Image:scan6.jpg|thumb|right|The Chemistry Condor Pool]]The job will be added to your list of jobs, and you can view its status, which is either '''running''' if there is a vacant slot in the queue you submitted to, or '''pending''' if there is not. Unfortunately, you cannot find out how many jobs are in front of yours for a pending job. If a module deadline is approaching, everyone will be submitting jobs, so it is very much in your interest to submit jobs early rather than at the last possible moment! Be aware that the time taken to run a Gaussian job depends critically on the size of the molecule, it scaling at around N4, where N is the number of (non-hydrogen) atoms. Typically, a molecule with around 12 (non-H) atoms will take around 30 minutes, but one with 24 would take around eight hours (or more depending on how ''floppy'' it is, and what kind of basis set you have requested). Calculations of optical rotations also take a long time.
*[[Image:scan8.jpg|thumb|right|Viewing the outputs]]When the job has completed, click on the '''Job List''' link. This will show all available outputs. Download the program Log file (this will help you chart whether the calculation was successfull) or the Gaussian Formatted Checkpoint file onto the desktop of the computer you are using. Double-click the file which should open up '''Gaussview''', where the molecule can be viewed and checked. You can use the latter file to e.g. plot molecular orbitals for the molecule, view vibrational modes, etc. Full details of these procedures are described in the [http://www.gaussian.com/g_tech/gv5ref/gv5ref_toc.htm Gaussview] and [http://www.gaussian.com/g_tech/g_ur/g09help.htm Gaussian] manuals.

====Archiving the output into a digital repository ====

[[Image:Dspace-mod.jpg|thumb|right|Depositing an entry in DSpace]]A very recent innovation is the '''Institutional digital repository''', a resource for permanently archiving calculations, spectra and crystal structures. You can get a flavour of this by archiving your own calculation in the '''SPECTRa''' digital repository. To the right of the Portal display is a link termed '''Publish'''. If you click on this, and the calculation is actually in a state to be published (it may for example have failed for some reason) then appropriate ''metadata'' for the calculation is collected, and the collection deposited into the repository. From here, it can be retrieved in future, and it can also be cited in the manner of a DOI, i.e. '''http://dx.doi.org/10042/to-ABCD''' where ABCD are the four integers representing your deposition ID. In a Wiki, cite this in the form of {{DOI|10042/to-2253}}

====A Note on Publishing to D-Space ====

In order to publish to an archive, you must first select the archive you want to publish to:

1. Log in to the HPC

2. Click on "Profile" in the bottom left

3. Tick the "Publish to DSpace" box

4. Click "Update"

When you click "Publish" in your job list, your files will now publish to the archive you have chosen.

=== Retaining the Calculations ===

Do not delete any completed jobs from the submission pages until your report has been graded. You may be asked to show individual jobs (via the input, or outputs) if for example the calculation has not succeeded in the manner you expected and you would like feed back on this or any other errors.

Third year simulation experiment

2015-10-07T16:54:46Z

Mjbear: /* Getting Help */

'''<big>This is the optional experiment which may be chosen by any third year student. If you are looking for the compulsory simulation experiment for students studying chemistry with molecular physics, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of exotic materials under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we hope to give you a gentle introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

This course closely follows some of the ideas introduced in Professor Bresme's statistical thermodynamics lecture course. Do not worry if you are doing this experiment before the lectures begin, everything that you need to know to complete the experiment will be explained in these instructions. We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the college's [http://www3.imperial.ac.uk/ict/services/hpc high performance computing] facilities.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will have seen how the concepts of statistical physics introduced by Professor Bresme are needed to calculate thermodynamic quantities such as temperature and pressure in computer simulations, and you will see how computers can be used to validate those concepts.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

==Assessment==

At the end of this experiment you must submit a "report" in wiki form. You can find instructions on how to create the wiki page and edit it in the "Report Preparation" section of [[Mod:writeup#Report_Preparation|this page]]. Each section of the experiment has a number of tasks that you should complete, labelled '''<big>TASK</big>'''. If this is a mathematical exercise, your report should contain a short summary of the solution. If it is a graphical exercise, you should include the relevant image. Your report should explain briefly what you did in each stage of the experiment, and what your findings were. At the end of the experiment, you should send the link to your wiki report to n.jackson12@imperial.ac.uk.

'''<big> YOU MUST SUBMIT YOUR WIKI REPORT BY 12 NOON ON THE FINAL FRIDAY OF THE EXPERIMENT.</big>'''

==Getting Help==



'''<big>Remember that if you take a college laptop, you MUST return it between 12 and 1pm on the final Friday of the experiment.</big>'''

The demonstrator and assessor for this exercise is Niall Jackson (n.jackson12@imperial.ac.uk). He will be available in the second floor chemistry computer room between 1pm and 3pm on the first Monday of the experiment, and between 2pm and 3pm every other day. If you have questions outside of these times, you are of course welcome to send them by e-mail. 

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.

# [[Third year simulation experiment/Running your first simulation|Running your first simulation]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third_year_simulation_experiment/Calculating heat capacities using statistical physics|Calculating heat capacities using statistical physics]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

Third year simulation experiment

2015-10-07T16:53:24Z

Mjbear: /* Assessment */

'''<big>This is the optional experiment which may be chosen by any third year student. If you are looking for the compulsory simulation experiment for students studying chemistry with molecular physics, you will find it [[Third_year_CMP_compulsory_experiment|here]].</big>'''

==Introduction==

Computer simulation is widely used to study a huge variety of chemical phenomena, from the behaviour of exotic materials under extreme conditions to protein folding and the properties of biological systems such as lipid membranes. In this experiment, we hope to give you a gentle introduction to one of the most powerful methods for the simulation of chemical systems, '''molecular dynamics simulation'''.

This course closely follows some of the ideas introduced in Professor Bresme's statistical thermodynamics lecture course. Do not worry if you are doing this experiment before the lectures begin, everything that you need to know to complete the experiment will be explained in these instructions. We will begin with a brief overview of the fundamental theory behind the method, before you start running your own simulations of a simple liquid using the college's [http://www3.imperial.ac.uk/ict/services/hpc high performance computing] facilities.

At the end of this experiment, you will have performed your own simulations using state of the art software packages used by researchers all around the world, and used those simulations to calculate both structural and dynamic properties of a simple liquid. You will have seen how the concepts of statistical physics introduced by Professor Bresme are needed to calculate thermodynamic quantities such as temperature and pressure in computer simulations, and you will see how computers can be used to validate those concepts.

All of the information that you need to complete the experiment is provided in these wiki pages. We have also tried to provide links to external resources and relevant textbooks where possible — unless explicitly stated, reading these resources '''is not required'''; they are provided only as further information for those interested in the subject.

==Assessment==

At the end of this experiment you must submit a "report" in wiki form. You can find instructions on how to create the wiki page and edit it in the "Report Preparation" section of [[Mod:writeup#Report_Preparation|this page]]. Each section of the experiment has a number of tasks that you should complete, labelled '''<big>TASK</big>'''. If this is a mathematical exercise, your report should contain a short summary of the solution. If it is a graphical exercise, you should include the relevant image. Your report should explain briefly what you did in each stage of the experiment, and what your findings were. At the end of the experiment, you should send the link to your wiki report to n.jackson12@imperial.ac.uk.

'''<big> YOU MUST SUBMIT YOUR WIKI REPORT BY 12 NOON ON THE FINAL FRIDAY OF THE EXPERIMENT.</big>'''

==Getting Help==

For help with the chemistry department laptops, visit [[Mod:laptop]].

'''<big>Remember that if you take a college laptop, you MUST return it between 12 and 1pm on the final Friday of the experiment.</big>'''

The demonstrator and assessor for this exercise is Niall Jackson (n.jackson12@imperial.ac.uk). He will be available in the second floor chemistry computer room between 1pm and 3pm on the first Monday of the experiment, and between 2pm and 3pm every other day. If you have questions outside of these times, you are of course welcome to send them by e-mail. The computational teaching fellow, Joao Bettencourt Cepeda Malhado (malhado@imperial.ac.uk), will be available in the same location between 1pm and 2pm daily.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.

# [[Third year simulation experiment/Running your first simulation|Running your first simulation]]
# [[Third year simulation experiment/Introduction to molecular dynamics simulation|Introduction to molecular dynamics simulation]]
# [[Third_year_simulation_experiment/Equilibration|Equilibration]]
# [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]]
# [[Third_year_simulation_experiment/Calculating heat capacities using statistical physics|Calculating heat capacities using statistical physics]]
# [[Third year simulation experiment/Structural properties and the radial distribution function|Structural properties and the radial distribution function]]
# [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]]

Programming a 2D Ising Model

2015-10-07T16:51:02Z

Mjbear: /* Assessment */

'''<big>This is the compulsory experiment for students taking the chemistry with molecular physics option. If you are looking for the optional simulation experiment for other third year chemistry students, you will find it [[Third_year_simulation_experiment|here]].</big>'''

==Introduction==

Last year, you were introduced to [https://www.python.org/ Python], a scripting language which is rapidly becoming the de facto language for everyday scientific programming. Python is an interpreted, rather than compiled language, and is rather more forgiving than older languages such as C or FORTRAN. This reduces the amount of time that we need to spend programming and debugging. The downside to all this is that the execution of a Python program is much slower than a compiled equivalent. As a compromise, we usually let large codes written in a compiled language (usually C/C++) do the hefty numerical work for us, and then use scripting languages like Python to analyse the results.

These large codes for numerical work (you may have already used GAUSSIAN for electronic structure calculations) typically take arcane text files as input, and produce equally arcane text files as output. If, for the sake of example, you run twenty different molecular dynamics simulations, and each of them produces an output file which contains information about the density of the system, then extracting this information by hand would be very tedious (and if you run hundreds or thousands of simulations, virtually impossible), but this sort of task is the thing at which languages like Python really excel.

In this exercise, you are going to use the Python that you learned last year to write a code perform Monte-Carlo simulations of the 2D [http://en.wikipedia.org/wiki/Ising_model Ising model], a set of spins on a lattice which is used to model ferromagnetic behaviour, and also to analyse the results of the simulation to find the heat capacity of the system and the Curie temperature — the temperature below which the system is able to maintain a spontaneous magnetisation.

==Assessment==

At the end of this experiment you must submit a "report" in wiki form. You can find instructions on how to create the wiki page and edit it in the "Report Preparation" section of [[Mod:writeup#Report_Preparation|this page]]. Each section of the experiment has a number of tasks that you should complete, labelled '''<big>TASK</big>'''. If this is a mathematical exercise, your report should contain a short summary of the solution. If it is a graphical exercise, you should include the relevant image. Your report should explain briefly what you did in each stage of the experiment, and what your findings were. At the end of the experiment, you should send the link to your wiki report, '''as well as a fully annotated copy of any Python scripts that you produce''' to n.jackson12@imperial.ac.uk.

'''<big>YOU MUST SUBMIT YOUR WIKI REPORT BY 12 NOON ON THE FINAL FRIDAY OF THE EXPERIMENT.</big>'''


If you wish, you are welcome to do the experiment on your own computer. You will need the [https://store.continuum.io/cshop/anaconda/ Anaconda] scientific Python distribution (if you are a Windows or Mac user). You may ask for help with installing this, but it is not part of the experiment — students who have scientific questions will take priority.

==Getting Help==



The demonstrator and assessor for this exercise is Niall Jackson (n.jackson12@imperial.ac.uk). He will be available in the second floor chemistry computer room between 1pm and 3pm on the first Monday of the experiment, and between 2pm and 3pm every other day. If you have questions outside of these times, you are of course welcome to send them by e-mail.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.

# [[Third_year_CMP_compulsory_experiment/Introduction_to_the_Ising_model|Introduction to the Ising model]]
# [[Third_year_CMP_compulsory_experiment/Calculating the energy and magnetisation|Calculating the energy and magnetisation]]
# [[Third_year_CMP_compulsory_experiment/Introduction to Monte Carlo simulation|Introduction to the Monte Carlo simulation]]
# [[Third_year_CMP_compulsory_experiment/Accelerating the code|Accelerating the code]]
# [[Third_year_CMP_compulsory_experiment/The effect of temperature|The effect of temperature]]
# [[Third_year_CMP_compulsory_experiment/The effect of system size|The effect of system size]]
# [[Third_year_CMP_compulsory_experiment/Determining the heat capacity|Determining the heat capacity]]
# [[Third_year_CMP_compulsory_experiment/Locating the Curie temperature|Locating the Curie temperature]]

Programming a 2D Ising Model

2015-10-07T16:50:53Z

Mjbear: /* Assessment */

'''<big>This is the compulsory experiment for students taking the chemistry with molecular physics option. If you are looking for the optional simulation experiment for other third year chemistry students, you will find it [[Third_year_simulation_experiment|here]].</big>'''

==Introduction==

Last year, you were introduced to [https://www.python.org/ Python], a scripting language which is rapidly becoming the de facto language for everyday scientific programming. Python is an interpreted, rather than compiled language, and is rather more forgiving than older languages such as C or FORTRAN. This reduces the amount of time that we need to spend programming and debugging. The downside to all this is that the execution of a Python program is much slower than a compiled equivalent. As a compromise, we usually let large codes written in a compiled language (usually C/C++) do the hefty numerical work for us, and then use scripting languages like Python to analyse the results.

These large codes for numerical work (you may have already used GAUSSIAN for electronic structure calculations) typically take arcane text files as input, and produce equally arcane text files as output. If, for the sake of example, you run twenty different molecular dynamics simulations, and each of them produces an output file which contains information about the density of the system, then extracting this information by hand would be very tedious (and if you run hundreds or thousands of simulations, virtually impossible), but this sort of task is the thing at which languages like Python really excel.

In this exercise, you are going to use the Python that you learned last year to write a code perform Monte-Carlo simulations of the 2D [http://en.wikipedia.org/wiki/Ising_model Ising model], a set of spins on a lattice which is used to model ferromagnetic behaviour, and also to analyse the results of the simulation to find the heat capacity of the system and the Curie temperature — the temperature below which the system is able to maintain a spontaneous magnetisation.

==Assessment==

At the end of this experiment you must submit a "report" in wiki form. You can find instructions on how to create the wiki page and edit it in the "Report Preparation" section of [[Mod:writeup#Report_Preparation|this page]]. Each section of the experiment has a number of tasks that you should complete, labelled '''<big>TASK</big>'''. If this is a mathematical exercise, your report should contain a short summary of the solution. If it is a graphical exercise, you should include the relevant image. Your report should explain briefly what you did in each stage of the experiment, and what your findings were. At the end of the experiment, you should send the link to your wiki report, '''as well as a fully annotated copy of any Python scripts that you produce''' to n.jackson12@imperial.ac.uk.

'''<big>YOU MUST SUBMIT YOUR WIKI REPORT BY 12 NOON ON THE FINAL FRIDAY OF THE EXPERIMENT.</big>'''



If you wish, you are welcome to do the experiment on your own computer. You will need the [https://store.continuum.io/cshop/anaconda/ Anaconda] scientific Python distribution (if you are a Windows or Mac user). You may ask for help with installing this, but it is not part of the experiment — students who have scientific questions will take priority.

==Getting Help==



The demonstrator and assessor for this exercise is Niall Jackson (n.jackson12@imperial.ac.uk). He will be available in the second floor chemistry computer room between 1pm and 3pm on the first Monday of the experiment, and between 2pm and 3pm every other day. If you have questions outside of these times, you are of course welcome to send them by e-mail.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.

# [[Third_year_CMP_compulsory_experiment/Introduction_to_the_Ising_model|Introduction to the Ising model]]
# [[Third_year_CMP_compulsory_experiment/Calculating the energy and magnetisation|Calculating the energy and magnetisation]]
# [[Third_year_CMP_compulsory_experiment/Introduction to Monte Carlo simulation|Introduction to the Monte Carlo simulation]]
# [[Third_year_CMP_compulsory_experiment/Accelerating the code|Accelerating the code]]
# [[Third_year_CMP_compulsory_experiment/The effect of temperature|The effect of temperature]]
# [[Third_year_CMP_compulsory_experiment/The effect of system size|The effect of system size]]
# [[Third_year_CMP_compulsory_experiment/Determining the heat capacity|Determining the heat capacity]]
# [[Third_year_CMP_compulsory_experiment/Locating the Curie temperature|Locating the Curie temperature]]

Programming a 2D Ising Model

2015-10-07T16:49:59Z

Mjbear: /* Getting Help */

'''<big>This is the compulsory experiment for students taking the chemistry with molecular physics option. If you are looking for the optional simulation experiment for other third year chemistry students, you will find it [[Third_year_simulation_experiment|here]].</big>'''

==Introduction==

Last year, you were introduced to [https://www.python.org/ Python], a scripting language which is rapidly becoming the de facto language for everyday scientific programming. Python is an interpreted, rather than compiled language, and is rather more forgiving than older languages such as C or FORTRAN. This reduces the amount of time that we need to spend programming and debugging. The downside to all this is that the execution of a Python program is much slower than a compiled equivalent. As a compromise, we usually let large codes written in a compiled language (usually C/C++) do the hefty numerical work for us, and then use scripting languages like Python to analyse the results.

These large codes for numerical work (you may have already used GAUSSIAN for electronic structure calculations) typically take arcane text files as input, and produce equally arcane text files as output. If, for the sake of example, you run twenty different molecular dynamics simulations, and each of them produces an output file which contains information about the density of the system, then extracting this information by hand would be very tedious (and if you run hundreds or thousands of simulations, virtually impossible), but this sort of task is the thing at which languages like Python really excel.

In this exercise, you are going to use the Python that you learned last year to write a code perform Monte-Carlo simulations of the 2D [http://en.wikipedia.org/wiki/Ising_model Ising model], a set of spins on a lattice which is used to model ferromagnetic behaviour, and also to analyse the results of the simulation to find the heat capacity of the system and the Curie temperature — the temperature below which the system is able to maintain a spontaneous magnetisation.

==Assessment==

At the end of this experiment you must submit a "report" in wiki form. You can find instructions on how to create the wiki page and edit it in the "Report Preparation" section of [[Mod:writeup#Report_Preparation|this page]]. Each section of the experiment has a number of tasks that you should complete, labelled '''<big>TASK</big>'''. If this is a mathematical exercise, your report should contain a short summary of the solution. If it is a graphical exercise, you should include the relevant image. Your report should explain briefly what you did in each stage of the experiment, and what your findings were. At the end of the experiment, you should send the link to your wiki report, '''as well as a fully annotated copy of any Python scripts that you produce''' to n.jackson12@imperial.ac.uk.

'''<big>YOU MUST SUBMIT YOUR WIKI REPORT BY 12 NOON ON THE FINAL FRIDAY OF THE EXPERIMENT.</big>'''

'''<big>IF YOU TAKE A COLLEGE LAPTOP, YOU MUST RETURN IT BY THE SAME TIME.</big>'''

If you wish, you are welcome to do the experiment on your own computer. You will need the [https://store.continuum.io/cshop/anaconda/ Anaconda] scientific Python distribution (if you are a Windows or Mac user). You may ask for help with installing this, but it is not part of the experiment — students who have scientific questions will take priority.

==Getting Help==



The demonstrator and assessor for this exercise is Niall Jackson (n.jackson12@imperial.ac.uk). He will be available in the second floor chemistry computer room between 1pm and 3pm on the first Monday of the experiment, and between 2pm and 3pm every other day. If you have questions outside of these times, you are of course welcome to send them by e-mail.

The member of academic staff responsible for this exercise is Professor Fernando Bresme (f.bresme@imperial.ac.uk).

==Structure of this Experiment==

This experimental manual has been broken up into a number of subsections. Direct links to each of them may be found below. You should attempt them in order, and you should complete all of them to finish the experiment.

# [[Third_year_CMP_compulsory_experiment/Introduction_to_the_Ising_model|Introduction to the Ising model]]
# [[Third_year_CMP_compulsory_experiment/Calculating the energy and magnetisation|Calculating the energy and magnetisation]]
# [[Third_year_CMP_compulsory_experiment/Introduction to Monte Carlo simulation|Introduction to the Monte Carlo simulation]]
# [[Third_year_CMP_compulsory_experiment/Accelerating the code|Accelerating the code]]
# [[Third_year_CMP_compulsory_experiment/The effect of temperature|The effect of temperature]]
# [[Third_year_CMP_compulsory_experiment/The effect of system size|The effect of system size]]
# [[Third_year_CMP_compulsory_experiment/Determining the heat capacity|Determining the heat capacity]]
# [[Third_year_CMP_compulsory_experiment/Locating the Curie temperature|Locating the Curie temperature]]

Mod:phys3

2015-10-07T16:48:41Z

Mjbear:

See also: [[Mod:intro|General info]],  [[mod:programs|Programs]],  [http://www.gaussian.com/g_tech/gv5ref/gv5ref_toc.htm Gaussian Online User Manual] | [http://faculty.ycp.edu/~jforesma/educ/visual/index.html Visualization Tutorials]
= Module 3 =

In this set of computational experiments, you will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

There are two parts:

a) tutorial material: how to use the programs and methods,

b) more challenging examples, with guidelines but fewer explicit instructions.



''As a guideline, you should aim to complete part (a) in the first week of the experiment. Do not rush the tutorial material: once you have a good understanding of the computational techniques and how to work with the codes, you will find the remaining parts more straightforward and be better able to solve any problems you encounter. Try to write up sections on your wiki in outline as you go. Include the tutorial material in your write-up. If you are having problems, talk them through with a demonstrator or staff at the first opportunity.''

In the second year physical chemistry laboratory, you may have carried out dynamics calculations using model potential energy surfaces to explore transition states. In that computational experiment, the total energy could quickly be calculated for different geometries of a triatomic system using an analytical function of the atomic coordinates (for more information, see for example [http://books.google.com/books?id=T8IZ1aa_FRkC&pg=RA1-PA36&lpg=RA1-PA36&dq=%22lake+eyring%22&source=web&ots=OXY00lSZ7D&sig=Ld_MTNwNjUDNGzB_5w1IxaMBMPU&hl=en&sa=X&oi=book_result&resnum=7&ct=result here] and [http://www.rsc.org/ejarchive/DC/1979/DC9796700007.pdf here]).

In this experiment, you will be studying transition structures in larger molecules. There are no longer fitted formulae for the energy, and the molecular mechanics / force field methods that work well for structure determination cannot be used (in general) as they do not describe bonds being made and broken, and changes in bonding type / electron distribution. Instead, we use molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface. As well as showing what transition structures look like, reaction paths and barrier heights can also be calculated.

==The Cope Rearrangement Tutorial==



''This part of the module is described as a 'tutorial' because it's an introduction to various computational techniques for locating transition structures on potential energy surfaces. It's different to the [[mod:gv_basic |GaussView Tutorial]] you can work through: it's an exercise where you're given specific instructions, then see if you can follow them, and also determine whether there are problems or better ways of carrying the exercise out. Please include this part in your write-up. Marks will be given for correct answers, the documentation showing how you got these, discussion, and how you went about solving any problems you encountered.''

In this tutorial we will use the Cope rearrangement of 1,5-hexadiene as an example of how to study a chemical reactivity problem.

Your objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

This [3,3]-sigmatropic shift rearrangement has been the subject of numerous experimental and computational studies (e.g. Houk et al. {{DOI|10.1021/ja00101a078}}), and for a long time its mechanism (concerted, stepwise or dissociative) was the subject of some controversy. Nowadays it is generally accepted that the reaction occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy. The B3LYP/6-31G* level of theory has been shown to give activation energies and enthalpies in remarkably good agreement with experiment. In this tutorial we will show how these can be calculated using Gaussian.

 

{| align="center"
|- align="center"
|
[[Image:pic2a.jpg]]
|
[[Image:pic2b.jpg]]
|- align="center"
| align="center" | ''Chair Transition State''
| align="center" | ''Boat Transition State''
|}

 

===Optimizing the Reactants and Products===

'' In this section you will learn how to optimize a structure, symmetrize it to find its point group, calculate and visualize vibrational frequencies and correct potential energies in order to compare them with experimental values. It is assumed that you are already familiar with using the builder in GaussView. ''

 

(a) Using GaussView, draw a molecule of 1,5-hexadiene with an "anti" linkage (approximately a.p.p conformation) for the central four C atoms . Clean the structure using the '''Clean''' function under the '''Edit''' menu.

Now we will optimize the structure at the '''HF/3-21G''' level of theory. Select '''Gaussian''' under the '''Calculate''' menu, click on the '''Job Type''' tab and choose '''Optimization'''. The default method should already be Hartree Fock and the default basis set is 3-21G, so there should be no need to change these. You can check this by clicking on the '''Method''' tab. Submit the job by clicking on the '''Submit''' button at the bottom of the window and give the job a meaningful name (e.g. react_anti).

When the job has finished, you will be asked if you want to open a file. Select '''Yes''' and choose the checkpoint (chk) file with the name of the job you have just run (e.g. react_anti.chk). This checkpoint file is a binary file that stores data calculated by Gaussian. The name of the chk file should have been assigned by default. Once the file has been opened, click on the '''Summary''' button under the '''Results''' menu and make a note of the energy.


Does your final structure have symmetry? Select '''Symmetrize''' under the '''Edit''' menu (note that sometimes it is necessary to relax the search criteria under the '''Point Group''' menu). Make a note of the point group.

 

(b) Now draw another molecule of 1,5-hexadiene with a "gauche" linkage for the central four C atoms. Would you expect this structure to have a lower or a higher energy than the anti structure you have just optimized? Optimize the structure at the '''HF/3-21G''' level of theory and compare your final energy with that obtained in (a). Again, check if the molecule has symmetry and make a note of the point group.

 

(c) Normally, calculated activation energies and enthalpies use the lowest energy conformation of a reactant molecule as a reference. Based on your results from above, try to predict what the lowest energy conformation of 1,5-hexadiene might be. Test out your hypothesis by drawing the structure and optimizing it.

 

(d) A table containing the low energy conformers of 1,5-hexadiene and their point groups is shown in [[Mod:phys3#Appendix 1|Appendix 1]]. Compare the structures that you have optimized with those in the table and see if you can identify your structure.

 

(e) Draw the Ci ''anti2'' conformation of 1,5-hexadiene (unless you have already located it). Optimize it at the '''HF/3-21G''' level of theory and make sure it has Ci symmetry. Compare your final energy to the one given in the table.


 

(f) When you are happy that your structure is the same as the one in the table, reoptimize it at the '''B3LYP/6-31G*''' level (6-31G* is equivalent to 6-31G(d) by selecting '''DFT''' under the '''Method''' menu and '''B3LYP''' from the box with the functionals on the right-hand side. Now select '''Link 0''' and change the name of the chk file to the name of the DFT optimization that you are about to run. Note that it is always advisable to do this when re-using or modifying existing structures to ensure that the original chk file is not overwritten. Run the job and make a note of the energy. Now compare the final structures from the '''HF/3-21G''' calculation with that at the higher level of theory. How much does the overall geometry change?

 

(g) The final energies given in the output file represent the energy of the molecule on the bare potential energy surface. To be able to compare these energies with experimentally measured quantities, they need to include some additional terms, which requires a frequency calculation to be carried out. The frequency calculation can also be used to characterize the critical point, i.e. to confirm that it is a minimum in this case: that all vibrational frequencies are real and positive.

Starting from your optimized B3LYP/6-31G* structure, run a frequency calculation at the same level of theory. You can do this by selecting '''Frequency''' under the '''Job Type''' tab. Ensure that the method is still correctly specified under the '''Method''' tab (''caution: on Windows, sometimes 'scrf=(solvent=water,check)' is incorrectly added!'') and then change the name of the chk file under the '''Link 0''' tab to the name of the frequency job that you are about to run. Run the job. Once the job has finished, open the log file this time. Select '''Vibrations''' under the '''Results''' menu. A list of all the vibrational frequencies modes should appear. Check that there are no imaginary frequencies, only real ones. You can visualize some of these vibrations under this menu and simulate the infrared spectrum.


Now, select '''View File''' under the '''Results''' menu and open the output file in the visualizer. Scroll down to the section beginning '''Thermochemistry'''. Under the vibrational temperatures a list of energies should be printed. Make a note of (i) the sum of electronic and zero-point energies, (ii) the sum of electronic and thermal energies, (iii) the sum of electronic and thermal enthalpies, and (iv) the sum of electronic and thermal free energies. The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS). It is important to make sure that you select the correct energy/enthalpy term to compare to your experimental values. Note that these corrections can also be calculated at other temperatures using the '''Temperature''' option in Gaussian, If you have time, try to re-calculate these quantities at 0 K as shown in the [[mod:gv_advanced | Advanced GaussView Tutorial]].

 

===Optimizing the "Chair" and "Boat" Transition Structures ===

'' In this section you will learn how to set up a transition structure optimization (i) by computing the force constants at the beginning of the calculation, (ii) using the redundant coordinate editor, and (iii) using QST2. You will also visualize the reaction coordinate and run the IRC (Intrinisic Reaction Coordinate) and calculate the activation energies for the Cope rearrangement via the "chair" and "boat" transition structures. ''

 

The "chair" and "boat" transition structures for the Cope rearrangement are shown in [[Mod:phys3#Appendix 2|Appendix 2]]. Both consist of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

 

(a) Draw an allyl fragment (CH2CHCH2) and optimize it using the '''HF/3-21G''' level of theory. Your structure should look like one half of the transition structures shown below.

Now open a new GaussView window by going to the '''File''' menu and selecting '''New''' and then '''Create MolGroup'''. Copy the optimized allyl structure from the first calculation by selecting '''Copy''' under the '''Edit''' menu, and then paste it twice into the new window by selecting '''Paste''' and then '''Append Molecule'''. Now orient the two fragments so that they look roughly like the chair transition state below by using the '''Shift Alt keys + Left Mouse button''' to translate one fragment with respect to the other and the '''Alt key + Left Mouse button''' to rotate it. The distance between the terminal ends of the allyl fragments should be approximately 2.2 Å apart. Save this structure to a Gaussian input file with a meaningful name (e.g. chair_ts_guess).

We are now going to optimize this transition state manually in two different ways. Transition state optimizations are more difficult than minimizations because the calculation needs to know where the negative direction of curvature (i.e. the reaction coordinate) is. If you have a reasonable guess for your transition structure geometry, then normally the easiest way to produce this information is to compute the force constant matrix (also known as the Hessian) in the first step of the optimization which will then be updated as the optimization proceeds. This is what we will try to do in the next section. However, if the guess structure for the transition structure is far from the exact structure, then this approach may not work as the curvature of the surface may be significantly different at points far removed from the transition structure. In some cases, a better transition structure can be generated by freezing the reaction coordinate (using '''Opt=ModRedundant''' and minimizing the rest of the molecule. Once the molecule is fully relaxed, the reaction coordinate can then be unfrozen and the transition state optimization is started again. One advantage of doing this, is that it may not be necessary to compute the whole Hessian once this has been done, and just differentiating along the reaction coordinate might give a good enough guess for the initial force constant matrix. This can save a considerable amount of time in cases where the force constant calculation is expensive.

 

(b) Use Hartree Fock and the default basis set 3-21G for parts (b) to (f).

Create a new MolGroup ('''File → New → Create MolGroup''') and copy and paste your guess structure into the window. Now set up a Gaussian optimization for a transition state. Go to the '''Gaussian''' menu under '''Calculate''' and click on the '''Job Type''' tab. Select '''Opt+Freq''' and then change '''Optimization to a Minimum''' to '''Optimization to a TS (Berny)'''. Choose to calculate the force constants '''Once''' and in the Additional keyword box at the bottom, type '''Opt=NoEigen'''. The latter stops the calculation crashing if more than one imaginary frequency is detected during the optimization which can often happen if the guess transition structure is not good enough. Submit the job. If the job completes successfully, you should have optimized to the structure shown in [[Mod:phys3#Appendix 2|Appendix 2]] and the frequency calculation should give an imaginary frequency of magnitude 818 cm-1. Animate the vibration and ensure that it is the one corresponding to the Cope rearrangement.

 

(c) Now we will try optimizing the transition structure again using the frozen coordinate method. Create a new MolGroup ('''File → New → Create MolGroup''') and copy and paste your guess structure into the window again. Now select '''Redundant Coord Editor''' from the '''Edit''' menu. Click on the highlighted file icon at the top left-hand corner (Create a New Coordinate) and a line should appear below saying '''Add Unidentified (?, ?, ?, ?)'''. Now go back to the GaussView window and select two of the terminal carbons from the allyl fragments which form/break a bond during the rearrangement. Return to the coordinate editor and select '''Bond''' instead of '''Unidentified''' and select '''Freeze Coordinate''' instead of '''Add'''. Now click on the icon again to generate another coordinate. This time select the opposite two terminal atoms and again select '''Bond''' and '''Freeze Coordinate'''. Click OK. Now set up the optimization as if it were a minimum and you should see the option '''Opt=ModRedundant''' already included in the input line. Submit the job.

'''Note:''' GaussView allows you to produce an input file with the frozen coordinate specified as e.g. <tt>B 5 1 2.200000 F</tt>. Unfortunately, a recent update to the Gaussian program means it does not recognise this syntax, and just ignores this line. This means that the coordinate ends up being optimised rather than frozen. Therefore do not use this method, but ensure the guess structure has suitable guess transition bond distances(~2.2 Å) using the ''Modify Bond'' tool in GaussView --[[User:Rzepa|Rzepa]] 14:39, 29 October 2012 (UTC)

'''Note 2:''' If you set the coordinate distance (i.e. B 5 1 2.2 B) and freeze it (i.e. B 5 1 F) as separate inputs to the modredundant editor, it appears to work as expected. (Lee)

 

(d) When the job has finished, open the chk file. You should find that the optimized structure looks a lot like the transition you optimized in section (b), except the bond forming/breaking distances are fixed to 2.2 Å. Now we are going to optimize them too. Open the '''Redundant Coord Editor''' from the '''Edit''' menu again and create a new coordinate as before by clicking on the icon, Select one of the bonds that was previously frozen and this time choose '''Bond''' instead of '''Unidentified''' and '''Derivative''' instead of '''Add'''. Repeat the procedure for the other bond. This time you need to set up a transition state optimization but we are not going to calculate the force constants as we did in section (b) (so we leave this option as '''Never'''), instead we will use a normal guess Hessian modified to include the information about the two coordinates we are differentiating along. Change the name of the chk file in '''Link 0''' if you do not want to write over the previous calculation and submit the job. When the calculation has finished, open the chk file, check the bond forming/bond breaking bond lengths and compare the structure to the one you optimized in section (b).

 

(e) Now we will optimize the boat transition structure. We will do this using the '''QST2''' method. In this method, you can specify the reactants and products for a reaction and the calculation will interpolate between the two structures to try to find the transition state between them. You must make sure that your reactants and products are numbered in the same way. Therefore, although our reactants and products are both 1,5-hexadiene, we will need to manually change the numbering for the product molecule so that it corresponds to the numbering obtained if our reactant had rearranged.

e.g.

<center>[[Image:pic3.jpg|200px]]</center>

Open the chk file corresponding to the optimized Ci reactant molecule (''anti2'' in [[Mod:phys3#Appendix 1|Appendix 1]]). Now open a second window and create a new MolGroup. Copy the optimized reactant molecule into the new window. In the same window, now select '''File → New → Add to MolGroup'''. The original molecule should disappear and a green circle should appear at the top left-hand corner with a '''2''' next to it. Clicking on the down arrow by the '''2''' will take you back to the original window and you will see your molecule again. This is how we read multiple geometries into GaussView. Go back to window '''2''', and copy and paste the reactant molecule a second time. This is going to be the product molecule and will be the molecule on which we need to change the numbering. If you now click on the icon showing two molecules side by side, then you can view both molecules simultaneously.

Now go to the '''View''' menu and select '''Labels''' so that you can see the numbering on both structures. Orient the two structures separately so they look something like the following:

{| align="center"
|- align="center"
|
[[Image:pic4a.jpg|200px]]
|
[[Image:pic4b.jpg|200px]]
|- align="center"
| align="center" | ''Reactant''
| align="center" | ''Product''
|}

 

Now click on the product structure. Go to the '''Edit''' menu and select '''Atom List'''. Starting from Atom 1 on the reactant, go through and renumber all the atoms on the Product so that they match the reactant molecule, e.g. for the numbering above you would start by changing atom '''6''' on the product molecule to atom '''3'''. The other atom numbers will update as you do this so make sure you do it in the correct order. (Note: Start numbering at 1 and go up, i.e. do not order 5 before 3 to avoid problems with the numbers updating --[[User:Jrc10|Jrc10]] 15:13, 31 January 2013 (UTC)) At the end, the numbering on your two molecules should correspond to each other in the following way:

 

{| align="center"
|- align="center"
|
[[Image:pic5a.jpg|200px]]
|
[[Image:pic5b.jpg|200px]]
|- align="center"
| align="center" | ''Reactant''
| align="center" | ''Product''
|}

 

Now we will set up the first '''QST2''' calculation. Go to the '''Gaussian''' menu and select '''Job Type''' as '''Opt+Freq''', and optimize to a transition state. This time you will have two options - '''TS (Berny)''' which we used in the previous calculations and '''TS (QST2)'''. Select '''TS (QST2)'''. Submit the job.

You will find that the job fails. To see why, open the chk file you created and view the structure. You will see that it looks a bit like the chair transition structure but more dissociated. In fact when the calculation linearly interpolated between the two structures, it simply translated the top '''allyl''' fragment and did not even consider the possibility of a rotation around the central bonds. It is clear that the QST2 method is never going to locate the boat transition structure if we start from these reactant and product structures.

Now go back to the original input file where you set up your QST2 calculation. We will now modify the reactant and product geometries so that they are closer to the boat transition structure. Click on the reactant molecule first and select the central '''C-C-C-C''' dihedral angle (i.e. '''C2-C3-C4-C5''' for the molecule above) and change the angle to 0o. Then select the inside '''C-C-C''' (i.e. '''C2-C3-C4''' and '''C3-C4-C5''' for the molecule above) and reduce them to 100o. Do the same for the product molecule. Your reactant and product molecules should now look like the following:

 

{| align="center"
|- align="center"
|
[[Image:pic6a.jpg|200px]]
|
[[Image:pic6b.jpg|200px]]
|- align="center"
| align="center" | ''Reactant''
| align="center" | ''Product''
|}

 

Set up the QST2 calculation again, renaming both the chk file under '''Link 0''' and the input file. Run the job again. This time it should converge to the boat transition structure. Check that there is only one imaginary frequency and visualize its motion.

The object of this exercise is to illustrate that although the QST2 method is has some advantages because it is fully automated, it can often fail if your reactants and products are not close to the transition structure. There is another method, the '''QST3''' method, that allows you to input the geometry of a guess transition structure also and this can often be more reliable. If you have time, you can try generating a guess boat transition structure and see if you can get the calculation to converge using the original reactant and product molecules. Remember to check the atom numbers in the transition structure are in the right order.

 

(f) Take a look at your optimized chair and boat transition structures. Which conformers of 1,5-hexadiene do you think they connect? You will find that it is almost impossible to predict which conformer the reaction paths from the transitions structures will lead to. However, there is a method implemented in Gaussian which allows you to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface. This is called the '''Intrinsic Reaction Coordinate''' or '''IRC''' method. This creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.

Open the chk file for one of your optimized chair transition structures. Under the '''Gaussian''' menu, select '''IRC''' under the '''Job Type''' tab. You will be presented with a number of options. The first is to decide whether to compute the reaction coordinate in one or both directions. As our reaction coordinate is symmetrical, we will only choose to compute it in the forward direction. Normally you would do both forward and reverse, either in one job or in two separate jobs. You are also given the option to calculate the force constants once, at every step along the IRC or to read them from the chk file, in this case choose calculate always. You would use the latter option if you have previously run a frequency calculation.

The final option to consider is the number of points along the IRC. The default is '''6''' but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under '''Link 0''' and submit the job. The job will take a while so now is a good time to take a coffee break...

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the '''B3LYP/6-31G*''' level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different.

As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program '''FreqChk''' to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The '''FreqChk''' utility program can be accessed from '''Gaussian09W'''. Launch '''Gaussian09W'''. Select '''utilities''' from the menu and click on '''FreqChk''' to launch the utility program. You will be prompted for a chk file. Follow the instructions from this [http://www.gaussian.com/g_tech/g_ur/u_freqchk.htm web link] to proceed.

 

=== Appendix 1 ===

 

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees HF/3-21G'''
| width="200" | '''Relative Energy/kcal/mol'''
|- align="center"
| ''gauche''
|
[[Image:gauche1.jpg|150px]]
| C2
| -231.68772
| 3.10
|- align="center"
| ''gauche2''
|
[[Image:gauche2.jpg|150px]]
| C2
| -231.69167
| 0.62
|- align="center"
| ''gauche3''
|
[[Image:gauche3.jpg|150px]]
| C1
| -231.69266
| 0.00
|- align="center"
| ''gauche4''
|
[[Image:gauche4.jpg|150px]]
| C2
| -231.69153
| 0.71
|- align="center"
| ''gauche5''
|
[[Image:gauche5.jpg|150px]]
| C1
| -231.68962
| 1.91
|- align="center"
| ''gauche6''
|
[[Image:gauche6.jpg|150px]]
| C1
| -231.68916
| 2.20
|- align="center"
| ''anti1''
|
[[Image:anti1.jpg|150px]]
| C2
| -231.69260
| 0.04
|- align="center"
| ''anti2''
|
[[Image:anti2.jpg|150px]]
| Ci
| -231.69254
| 0.08
|- align="center"
| ''anti3''
|
[[Image:anti3.jpg|150px]]
| C2h
| -231.68907
| 2.25
|- align="center"
| ''anti4''
|
[[Image:anti4.jpg|150px]]
| C1
| -231.69097
| 1.06
|}

 

=== Appendix 2 ===

{| cellpadding="5"
|- align="center"
|
[[Image:appendix2a.jpg|300px]]
|- align="center"
| ''C2h Chair Transition State''
|- align="center"
|- align="center"
|- align="center"
|
[[Image:appendix2b.jpg|300px]]
|- align="center"
| ''C2v Boat Transition State''
|}

 

=== Results Table ===

 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

 

==The Diels Alder Cycloaddition==

''In this exercise, you will characterise transition structures using any of the methods described above in the tutorial: the choice is up to you. In addition, you will look at the shape of some of the molecular orbitals. To help you structure your report, there is a data/discussion sheet at the end of this section.''

 

[[Image:mb_da1.jpg |right|thumb|Diels Alder cycloaddition]]
The Diels Alder reaction belongs to a class of reactions known as pericyclic reactions. The π orbitals of the dieneophile are used to form new σ bonds with the π orbitals of the diene. Whether or not the reactions occur in a concerted stereospecific fashion ('''allowed''') or not ('''forbidden''') depends on the number of π electrons involved. In general the HOMO/LUMO of one fragment interacts with the HOMO/LUMO of the other reactant to form two new bonding and anti-bonding MOs. The nodal properties allow one to make predictions according to the following rule:

''If the HOMO of one reactant can interact with the LUMO of the other reactant then the reaction is '''allowed'''.''

''The HOMO-LUMO can only interact when there is a significant overlap density. If the orbitals have different symmetry properties then no overlap density is possible and the reaction is '''forbidden'''.''

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

 

Shown on the right is a diagram of the transition state for the Diels-Alder reaction between ethylene and butadiene. The ethylene approaches the cis form of butadiene from above.
[[Image:mb_da2.jpg |right|thumb|Ethylene+Butadiene cycloaddition]]

Before beginning our quantitative study, it is helpful to discuss the interaction of the π orbitals in a simple qualitative way.

''You will confirm some of these considerations in your computations.''

The principal orbital interactions involve the π/ π* orbitals of ethylene and the HOMO/LUMO of butadiene. It is referred to as [4s + 2s] since one has 4 π orbitals in the π system of butadiene. The orbitals of ethylene and butadiene and ethylene can be classified as symmetric '''s''' or anti-symmetric '''a''' with respect to the plane of symmetry shown.

The HOMO of ethylene and the LUMO of butadiene are both '''s''' (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both '''a'''. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is '''a'''.

 

=== Exercise ===

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

i) Use GaussView to build cis butadiene, and optimize the geometry using Gaussian. Plot the HOMO and LUMO of cis butadiene and determine its symmetry (symmetric or anti-symmetric) with respect to plane.

''There are two ways to do this in GaussView. One is: Select '''Edit→MOs'''. Select the HOMO and the LUMO from the MO list (highlights it yellow). Click the button '''Visualise''' (not Calculation), then '''Update'''. Alternately, having calculated the surface for this orbital, you can display it in the main GaussView window for the molecule, from the '''Results→Surfaces''' menu. Select '''Surface Actions→Show Surface'''. Having displayed the surface this way, you can also select '''View→Display Format→Surface''', and change '''Solid''' to '''Mesh'''.''

 

ii) Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

[[Image:mb_da3.jpg |right|thumb|]]

The transition structure has an envelope type structure, which maximizes the overlap between the ethylene π orbitals and the π system of butadiene. One way to obtain the starting geometry is to build the bicyclo system (b) and then remove the -CH2-CH2- fragment. One must then guess the interfragment distance (dashed lines) and optimize the structure, but use any method you wish, based on the tutorial above, to characterise the transition structure. Confirm you have obtained a transition structure for the Diels Alder reaction!

[[Image:mb_da4.jpg |right|thumb|guessing the transition structure]]

Once you have obtained the correct structure, plot the HOMO as in (i). Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

 

(iii) To Study the regioselectivity of the Diels Alder Reaction

Cyclohexa-1,3-diene '''1''' undergoes facile reaction with maleic anhydride '''2''' to give primarily the endo adduct. The reaction is supposed to be kinetically controlled so that the exo transition state should be higher in energy.

[[Image:Bearpark_pic_edit_by_jm906.JPG |right|thumb|regioslectivity]]

Locate the transition structures for both 3 and 4. Compare the energies of the endo and exo forms.

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?

 

=== Suggested Discussion ===

Use this template as a guide. Screen images can be saved from the GaussView '''File''' menu.

''For cis butadiene'': 
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

''For the ethylene+cis butadiene transition structure'': 
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state.
Is the formation of the two bonds synchronous or asynchronous?
How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure '''s''' or '''a'''?

Which MOs of butadiene and ethylene have been used to form this MO?
Explain why the reaction is allowed.

''For the cyclohexa-1,3-diene reaction with maleic anhydride'': 
Give the relative energies of the exo and endo transition structures.
Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
(There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

''Further discussion'': 
What effects have been neglected in these calculations of Diels Alder transition states?

Look at published examples and investigate further if you have time.
(e.g. {{DOI|10.1021/jo0348827}})

----


© 2008-2013, Imperial College London

Main Page

2015-10-07T16:46:22Z

Mjbear: /* Third Year Computational Chemistry Lab */

[[Image:QR_complab.png|right|QR]]
= {{fontcolor1|yellow|black|Chemistry}}{{fontcolor1|orange|black|@}}{{fontcolor1|purple|white|www.ch.imperial.ac.uk}} =
This is a communal area for documenting teaching and laboratory courses. To [[admin:add|add to any content on these pages]], you will have to log in using your Imperial College account.
== ChemDraw/Chemdoodle Hints ==
#[[IT:chemdraw|Useful hints for using ChemDraw/ChemDoodle]]

== Student wiki ==
#[[StudentWiki:Contents|Student pages]]

== Tablet Project ==
# [[tablet:tablet|Tablet Pilot Project]]
== 3D ==
# [[mod:3D|3D-printable models]]
# [[mod:stereo|Lecture Theatre Stereo]]

= Laboratories and Workshops =
== First Year ==
=== [[it:it_facillities|Email and IT@www.ch.imperial.ac.uk]]: A summary of available IT resources ===

===First Year Chemical Information Lab 2014 ===
*[[it:intro-2011|Introduction]]
*[[it:lectures-2011|Lectures]]
*[[it:coursework-2011|Coursework]]
*[[it:assignment-2011|Assignment for the course]]
*[[it:software-2011|List of software for CIT]]
*[[it:searches-2011|Search facilities for CIT]]
*[[Measurement_Science_Lab:_Introduction|Measurement Science Lab Course]]

===[[organic:conventions|Conventions in organic chemistry]]===
===[[organic:arrow|Reactive Intermediates in organic chemistry]]===
===[[organic:stereo|Stereochemical models]] ===

== Second Year ==
===Second Year Modelling Workshop ===
*[[Coursework]]
*[[Second Year Modelling Workshop|Instructions]] and [[mod:further_coursework|Further optional coursework]]
*[[it:conquest|Conquest searches]]




=== Molecular Dynamics (Physical Chemistry Laboratory) ===
*[[Running MD code in MATLAB|Running MD code in MATLAB]]

== Third Year ==

===Third Year Computational Chemistry Lab ===
*[[mod:intro|Information needed for the course]]


*[[mod:writeup|Report writing and submission]]

*[[mod:latebreak|Late breaking news]]
*The course modules

**[[Mod:phys3|Transition states and reactivity.]]
**[[ThirdYearMgOExpt-1415|MgO experiment]]
** [[Third_year_CMP_compulsory_experiment|CMP compulsory experiment: Programming for liquid simulation]]
** [[Third_year_simulation_experiment|Optional experiment: Simulation of a simple liquid]]
*[[mod:programs|General program instructions:]]
**[[mod:gaussview|The Gaussview/Gaussian suite]]
**[[Mod:scan|Submitting jobs to the chemistry high-performance-computing resource]]

= Online materials for mobile devices =
# [[ebooks:howto|How to get eBooks]]
# [https://play.google.com/store/apps/details?id=com.blackboard.android&hl=en Blackboard mobile learn for Android]
# [https://itunes.apple.com/us/app/blackboard-mobile-learn/id376413870?mt=8 Blackboard mobile learn for iOS]
# [https://itunes.apple.com/gb/course/id562191620 Pericylic reactions in iTunesU ] (download [https://itunes.apple.com/gb/app/itunes-u/id490217893?mt=8 App] first)
# [https://itunes.apple.com/gb/course/id562191825 Conformational analysis in iTunesU] (download [https://itunes.apple.com/gb/app/itunes-u/id490217893?mt=8 App] first)
# [https://itunes.apple.com/gb/course/id562191342 A library of mechanistic animations in iTunesU] (download [https://itunes.apple.com/gb/app/itunes-u/id490217893?mt=8 App] first)
# [[IT:panopto|How to compress and disseminate Panopto lecture recordings]]
= Material from previous years =
== First year ==
===Introduction to Chemical Programming Workshop 2013===
*[[1da-workshops-2013-14|Workshop script]]


= PG =

# [[rdm:intro|Data management]]

Mod:writeup

2015-10-07T16:45:40Z

Mjbear:

See also: [[Mod:Cheatsheet|Cheatsheet]].

== The expected length of the report ==
A Wiki does not have pages as such. But as a very rough guide, expect to produce something the equivalent of about six printed pages (although you can invoke ''pop-ups'' and the like which make a page count only very approximate). Use graphics reasonably sparingly, and to the point.

= Why Wiki? =
Since everyone is used to using [http://www.wordonwiki.com Microsoft Word], why do we [[talks:rzepa2011|use a Wiki]] for this course? Well, the Wiki format has several advantages.
#A full revision and fully dated history across sessions is kept (Word only keeps this during a session). This is more suited for laboratory work, where you indeed might need to go back to a particular day and experiment to check your notes.
#The (chemistry) Wiki allows you to include molecule coordinates, vibrations and MO surfaces which can be rotated and inspected, along with other chemical extensions. Word does not offer this.
#The Wiki allows you to include "zoomable" graphics in the form of SVG (which Gaussview generates), and access to the 17-million large [http://commons.wikimedia.org/wiki/Main_Page WikiCommons] image library, as well as access to the Wikipedia InterWiki.
#The [[w::Help:Template|template]] concept allows pre-formated entry. There are lots of powerful [[w:Category:Chemical_element_symbol_templates|chemical templates]] available.
#Autonumbered referencing, and particularly cross-referencing, is actually easier than using Word.
#You (and the graders) can access your report anywhere online, it is not held on a local hard drive which you may not have immediate access to.
#It has automatic date and identity stamps for ALL components, which means we can assess that part of the report handed in by any deadline, and deal separately with anything which has a date-stamp past a given deadline. A Word document has only a single date-and-time stamp and so deadlines must apply to the whole document.
#And we have been using Wikis for course work since '''2006''', so there is lots of expertise around!
#And finally, Wiki is an example of a [http://en.wikipedia.org/wiki/Markdown MarkDown] language, one designed to facilitate writing using an easy-to-read, easy-to-write plain text format (with the option of converting it to structurally valid XHTML).

=Report Preparation =

== Before you start writing ==
Before you start writing, you might wish to read this article<ref name="adma.200400767">G.M. Whitesides, "Whitesides' Group: Writing a Paper", ''Advanced Materials'', '''2004''', ''16'', 1375–137 {{DOI|10.1002/adma.200400767}}</ref> (or perchance this advice<ref name="ac2000169">R. Murray, "Skillful writing of an awful research paper", ''Anal. Chem.'', '''2011''', ''83'', 633. {{DOI|10.1021/ac2000169}}</ref>). In your report you should discuss your evaluation of each of the techniques you use here. You should include at least '''three literature references in addition to the ones given here'''. You might also want to check the [[Mod:latebreak|late breaking news]] to see if there are any helpful hints about the project you might want to refer to. You will be writing your report in Wiki format, and it is best to do this continually as you do the experiment. In effect, your Wiki report is also your laboratory manual.

#[[File:Wiked.jpg|right|400px|WikED editor]]Open Firefox as a Web browser.
#There should be a tab for the course Wiki, but if not, use the URL '''www.ch.ic.ac.uk'''
#*[[Image:exception1.jpg|right|thumb|Security exception]]If the browser asks you to add a security exception, do so and proceed to '''view/confirm''' the certificate.
#You can view the Wiki without logging in, but to create a report, you will have to login as yourself. Check '''Remember my login on this computer'''
#Before you start, you might want to visit the [[Special:Preferences|preferences]] page to customise the Wiki for yourself.
#Follow the procedures below. Check that the WikED icon is present at the top, just to the right of the log out text (ringed in red). If you want a minimalist editing interface, click this icon to switch it off. A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.

=== Assigning your report an identifier ===
#*[[Image:New_report.jpg|right|400px|Creating a report page]] In the address box, type something like
#**'''wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:{{fontcolor1|yellow|black|XYZ1234}}'''
#*The characters '''Mod''' indicate a report associated with the modelling course, and '''{{fontcolor1|yellow|black|XYZ1234}}''' is your secret password for the report. It can be any length, but do not make it too long! It should then tell you there is no text in this page. If not, try another more unique password. You should now click on the '''edit this page''' link to start. Use a different address for each module of the course you are submitting.
#*It is a {{fontcolor1|yellow|black|good idea}} to add a bookmark to this page, so that you can go back to it quickly.
==== Assigning your report a persistent (DOI-style) identifier.====
Use [http://spectradspace.lib.imperial.ac.uk/url2handle/ this tool] to assign a shorter identifier for your report (one that can be invoked using eg <nowiki>{{DOI|shortidentifier]]</nowiki>.

=== Converters to the Wiki format ===
#Convert a Word document. Open it in '''OpenOffice''' (rather than the Microsoft version) and '''export''' as Mediawiki. Open the resulting .txt file in eg WordPad, select all the text, copy, and then paste this into the Wiki editing page. You will still have to upload the graphical images from the original Word document separately.
#There is also a [http://labs.seapine.com/htmltowiki.cgi HTML to Wiki] converter which you can use to import HTML code from an existing Web page into a (Media)Wiki.

== Basic editing ==
An [[Mod:inorganic_wiki_page_instructions|introductory tutorial]] is available which complements the information here.
*A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.
*[[Image:report12345.jpg|right|thumb|The editing environment]]You will need to create a separate report page on this Wiki for each module of the course. Keep its location private (i.e. do not share the URL with others).
*The WikED toolbar along the top of the page has a number of tools for:
**adding citation references,
**superscript and subscripting (the H2O WikEd symbol will automatically do this for a formula),
**creating tables
**adding links (Wiki links are internal, External links do what they say on the tin)
**# local to the wiki, as <nowiki>[[mod:writeup|text of link]]</nowiki>
**# remote, as <nowiki>[http://www.webelements.com/ text of link]</nowiki>
**# Interwiki, as <nowiki>[[w:Mauveine|Mauveine]]</nowiki>
**# DOI links are invoked using the DOI template <nowiki>{{DOI|..the doi string ..}}</nowiki> or the more modern form <nowiki>[[doi:..the dpi string..]]</nowiki>
**# Links to an Acrobat file you have previously uploaded to the Wiki can be invoked using this template: <nowiki>{{Pdf|tables_for_group_theory.pdf|...description of link ...}}</nowiki>
**# There are lots of other [[Special:UncategorizedTemplates|templates]] to make your life easier such as the [[w:Template:Chembox|ChemBox]]
**If you need some help, invoke it from the left hand side of this page.
*Upload all graphics files also with unique names (so that they do not conflict with other people's names). If you are asked to replace an image, '''REFUSE''' since you are likely to be over-writing someone else's image!
** Invoke such an uploaded file as <nowiki>[[image:nameoffile.jpg|right|200px|Caption]] </nowiki>
**We support WikiComons, whereby images from the [http://commons.wikimedia.org/wiki/Main_Page content (of ~10 million files)] from [http://meta.wikimedia.org/wiki/Wikimedia_Commons Wikimedia Commons Library] can be referenced for your own document. If there is a name conflict, then the local version will be used before the Wiki Commons one.
***To find a file, go to [http://commons.wikimedia.org/wiki/Main_Page Commons]
***Find the file you want using the search facility
***Invoke the top menu, '''use this file in a Wiki''', and copy the string it gives you into your Wiki page
*** <nowiki>[[File:Armstrong Edward centric benzene.jpg|thumb|Armstrong Edward centric benzene]]</nowiki>
*Colour can be added (sparingly) using this {{fontcolor1|yellow|black|text fontcolor}} template. (invoked as <nowiki>{{fontcolor1|yellow|black|text fontcolor}}</nowiki> )
*Save and preview constantly (this makes a new version, which you can always revert to). It goes without saying that you should not reference this page from any other page, or indeed tell anyone else its name.
*'''Important:''' Every 1-2 hours, you might also want to make a [[Mod:writeup#Backing_up_your_report|backup of your report]]. This is particularly important when adding Jmol material, since any error in the pasted code can result in XML errors. The current Wiki version does not flag these errors properly, but instead just hangs the page. Whilst you can try to [[Mod:writeup#Fixing_broken__Pages|repair the page]] as described below, it is much safer to also have a backup!
*You should get into the habit of recording results, and appropriate discussion, soon after they are available, in the manner of a laboratory note book.

== More Editing features ==
=== Handling References/citations with a DOI ===
This section shows how literature citations<ref name="jp027596s">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343. {{DOI|10.1021/ja9825332}}</ref> can be added to text<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref> using the '''<nowiki>{{DOI|value}}</nowiki>''' (digital object identifier) template to produce a nice effect. Citations can be easily added from the WikED toolbar.
*The following text is added to the wiki, exactly as shown here: '''<nowiki><ref name="ja9825332">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343.{{DOI|10.1021/ja9825332}}</ref></nowiki>'''
*Giving a reference a unique identifier, such as '''<nowiki><ref name="ja9825332"></nowiki>''' allows you to refer to the same footnote again by using a ref tag with the same name. The text inside the second tag doesn't matter, because the text already exists in the first reference. You can either copy the whole footnote, or you can use a terminated empty ref tag that looks like this: '''<nowiki><ref name="ja9825332" /></nowiki>'''.
*Collected citations will appear below wherever you place the '''<nowiki><references /></nowiki>''' tag, as here. If you forget to include this tag, the references will not appear!
==== Including the DOI for your experiment data ====
The datasets associated with your experiment can be given a DOI by '''publishing''' any entry in the [https://scanweb.cc.imperial.ac.uk/uportal2/ SCAN Portal]. You can include this DOI as a normal citation.<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref>

==== Additional citation handling ====
* A macro-based reference formatting program has been developed in Microsoft Excel to not only produce the wiki code for direct pasting into your report, but that '''''also''''' formats text for placing in documents, such as synthesis lab reports. This program is available [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Reference_Formatting_Program here].
* A '''[[Template:Cite_journal|Cite journal]] template''' is installed for anyone who wants to experiment
----

References and citations
<references />

----

=== Using an iPad ===

[https://itunes.apple.com/gb/app/wiki-edit/id391012741?mt=8 Wiki Edit] for IOS allows a Wiki to be edited using an iPad. You can dictate your text using '''Siri''' if your speed at '''thumb-typing''' is not what it should be.

= Bringing your report to life =
== Basic JSmol ==
You can use coordinate files created as part of your work (in CML or Molfile format) to insert rotating molecules for your page.
#Using your graphical program (ChemBio3D or Gaussview), '''save''' your molecule as an '''MDL File''', which has the extension '''.mol''', or as '''chemical markup language''', which has the extension '''.cml'''.
#Or, if your calculation ran on the SCAN batch system, '''publish''' the calculation, and in the resulting deposited space, download the .cml or the '''logfile.out''' file to be found there (the latter should be used for vibrations only).
#On the Wiki, '''Upload File''' (from the left hand panel) and select the molecule file you have just placed on your hard drive as above.
#On your Wiki page, insert <nowiki><jmolFile text="Explanatory text for link">BCl3-09.log</jmolFile></nowiki> where in this example, BCl3-09.log is the just uploaded file.
##The should produce <jmolFile text="this link">BCl3-09.log</jmolFile>. When clicked, it will open up a separate floating window for your molecule.
##Further actions upon the loaded molecule (such as selecting a vibrational mode and animating the vibration) are done by right-mouse clicking in the Jmol window.

#When using animations, please let them pop up in a separate window using the <jmolAppletButton> function. Your browser won't slow down and you will make your life so much simpler. =)
##Read more on how to do that [http://wiki.jmol.org/index.php/MediaWiki#Jmol_applet_in_a_popup_window here ]. --[[User:Rea12|Rea12]] 20:58, 8 September 2014 (BST)

== Advanced JSmol ==

A much more powerful invocation is as follows. The following allows a molecule to be directly embedded into the report, and it also shows how to put a script in to control the final display.
{| class="wikitable" border="2"
|-
! copy/paste either of the two sections below into your own Wiki
|-
|<pre><jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>yourmolecule.cml</uploadedFileContents>
</jmolApplet>
</jmol>


<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script><uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol></pre>
|-
! First molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])
|-
|<jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color><size>300</size>
<script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script>
<uploadedFileContents>pentahelicene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Second molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])

|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script>
<uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Every time you embed a molecule in a Wiki page in the above manner, the Web browser must set aside memory. Too many molecules, and the memory starts to run out, and the browser may slow down significantly. So use the feature sparingly, only including key examples where some structural feature would benefit from the rotational capabilities.
It is [http://chemapps.stolaf.edu/jmol/docs/ possible] to add many other commands to the JSmol container above. For example, '''<nowiki><script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script></nowiki>''' will colour atoms 3 4 and 5 (obtained by mouse-overs) purple, and then measure the length of the 3-5 bond. Further examples of how to invoke Jmol are [http://www.mediawiki.org/wiki/Extension:Jmol#Installing_Jmol_Extension found here], and a comprehensive list [http://chemapps.stolaf.edu/jmol/docs/ given here].

== Incorporating orbital/electrostatic potential isosurfaces ==
The procedure is as follows
# Run a Gaussian calculation on the SCAN
# When complete, select ''Formatted checkpoint file'' from the output files and download
# Double click on the file to load into Gaussview
##To generate a molecule orbital, '''Edit/MOs''' and select (= yellow) your required orbitals.
##* '''Visualise''' and '''Update''' to generate them
## To generate an electrostatic potential, '''Results/Surfaces and Contours''', then '''Cube Actions/New Cube/Type=ESP'''. This will take 2-3 minutes to generate
##* In '''Surfaces available''' pre-set the Density to '''0.02''' and then '''Surface Actions/New Surface'''. Try experimenting with the value of Density for the best result. Save the cube as per below.
# In '''Results/Surfaces and contours''' from the '''cubes available''' list, select one and '''Cube actions/save cube'''
# Invoke [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ this page] and you will be asked to select your cube file,
# followed by three file save dialogs, one for the coordinates (.xyz), one for the MO surface (.jvxl) and a shrink-wrapped bundle (.pngj).
# Insert the following code into your Wiki, replacing the file name with your own choice from the preceding file save dialogs.
<pre><nowiki><jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol></nowiki>
</pre>
# [[image:absolute_path.jpg|right|350px]]Next, upload these two files into the Wiki (one file at a time, the multiple file uploader does not seem to work for this task)
## Now for the tough bit. You will need to find the absolute path for the .jvxl file. Above, this appears as images/1/1b/AHB_mo22-2.cub.jvxl
## Just after uploading a .jvxl file, you will see a response as shown on the right.
## Right click on '''Edit this file using an external application'''. You can used any text editor (Wordpad etc).
## This text file will contain something like: <tt>; or go to the URL <nowiki>https://wiki.ch.ic.ac.uk/wiki/images/1/1b/AHB_mo22-2.cub.jvxl</nowiki></tt>
#Select just the string '''images/1/1b/AHB_mo22-2.cub.jvxl''' and paste it in as shown above:
#You should get something akin to:
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;
</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
* You can superimpose two surfaces. Change the script contents above to append a second surface to the first: <pre><script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;isosurface append color red blue "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script></pre>
* The four colours used in this line can be changed to whatever you consider appropriate.
=== An alternative way of loading surfaces ===
This method avoids the need to specify paths to files as seen above. Instead uses the '''.pngj''' bundle which contains all necessary information and can be invoked by
<pre><nowiki><jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile></nowiki></pre> which produces <jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile>.
# It only supports one surface (you cannot superimpose two orbitals)
# You can also load other surfaces, such as <jmolFile text="molecular electrostatic potentials">Checkpoint_60018_esp.cub.pngj‎</jmolFile> generated from a cube of electrostatic potential (ESP) values created using Gaussview as follows:
## Download .fchk file from SCAN
## Open using Gaussview
## '''Results/Surfaces & contours/Cube actions/New Cube/ESP''' and then '''cube actions/save cube''' which is how the above was generated. You may have to play around with the value of the density (~0.02).

=== MOPAC orbitals ===
# Run MOPAC from ChemBio3D, selecting '''Compute Properties/Molecular Surface''' from the '''properties''' pane, and in the '''General pane''' specify a location for the output and deselect '''Kill temporary files''' if not already so.
# Upload the '''.mgf''' file so produced to the Wiki
# Invoke as follows ('''MO 35;''' means the 35th most stable orbital for that molecule).
<pre><nowiki><jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>300</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol></nowiki></pre>
<jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>200</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol>

== Enhancing your report with Equations ==
*You may have need to express some [http://meta.wikimedia.org/wiki/Help:Formula equations] on the Wiki. This is currently supported only using a notation derived from '''LaTeX''', and as with the Jmol insertion above, is enabled within a '''<nowiki><math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math></nowiki>''' field inserted using the default editor (the SQRT(n) button), and producing the following effect:
<math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math>

The requisite syntax can be produced by using
*MathType as an equation editor (used standalone or in Word). It places the required LaTeX onto the clipboard for pasting into the Wiki).
*[http://www.lyx.org/ Lyx] which is a free stand-alone editor.
*A more general solution to this problem is simply to create a graphical image of your equation, and insert that instead as a picture.

== Inserting Tables ==
Instead of inserting screenshots of Excel, tables can be produced using MediaWiki markup (see [http://www.mediawiki.org/wiki/Help:Tables this page]), where you can also find lots of examples of different styles of table. However, this can be quite time consuming when you have a lot of tabulated data and need to copy it from somewhere like Excel into ChemWiki. Instead of typing it by hand, you can save your Excel worksheet as a comma separated file (.csv) and then use this [[http://area23.brightbyte.de/csv2wp.php CSV to MediaWiki markup]] convertor. Note that cells starting with "-", e.g. for negative numbers, need a space inserted between the - and | in the output otherwise MediaWiki interprets it as a new row.

Another web-based utility is available called [http://excel2wiki.net/ Excel2Wiki] which can be used to generate MediaWiki code from an Excel table.

== SVG (for display of IR/NMR/Chiroptical Spectra) ==
[[File:IR.svg|300px|right|SVG]]SVG stands for '''scaleable-vector-graphics'''. Its advantage is well, that it scales properly (but it has many others, including the ability to make simple edit to captions etc using Wordpad or similar). From your point of view, it is readily generated using Gaussview. If you view an '''IR/NMR/UV-vis/IRC/Scan/''' spectrum in this program, it allows you to export the spectrum as SVG (right-mouse-click on the spectrum to pull down the required menu). Upload this file, and invoke it as <nowiki>[[File:IR.svg|200px|right|SVG]]</nowiki> If you open eg IR.svg in Wordpad (or other text editor), you can edit the captions, font sizes etc (its fairly obvious). Oh, you will need to use a web browser that actually displays SVG. Internet Explorer 8 does not (9 is supposed to). Use Firefox/Chrome/Safari etc.

== Chemical Templates ==
An example is the [[w:Template:Chembox|ChemBox]]. Volunteers needed to test/extend these!

= Submitting your report =
For the '''combined synthetic and organic''' experiment submit your Wiki personal URL as obtained above to [mailto:Org-8@imperial.ac.uk?subject=Computational_lab_1C Org-8@ic.ac.uk] with a deadline of the Friday of the second week of any 2-week experiment at '''12noon'''.

For the '''Computational Chemistry Lab''': inorganic and physical submit your wiki URL address on Blackboard by 12:00 on the friday of the 2-week experiment.

= Backing up your report =
[[Image:export1.jpg|left|250px]][[Image:Export2.jpg|right|200px]]Invoke [[Special:Export|this utility]] to back your project up. In the box provided, enter e.g. '''Mod:wzyz1234''' being the password for your report. This will generate a page (right) which can be saved using the Firefox '''File/Save_Page_as''' menu. Specify '''Web Page, XML only''' as the format, and add .xml to the file suffix. You might want to do this eg on a daily basis to secure against corruption. This is in addition to the notes for how to repair broken pages.

The same file can now be reloaded using [[Special:Import|Import]].

= Fixing broken Pages =
There are several ways in which a page can break.

*We have had instances of people inserting a corrupted version of the Jmol lines into their project, resulting in a '''XML error''' or '''Database error'''. Recovering from such an error is not simple. So we do ask that you carefully check what you are pasting into the Wiki, and that its form is exactly as shown above. For example, below is a real example of inducing such an error. Can you see where the fault lies? (Answer: the <nowiki><jmol></nowiki> tag is not matched by <nowiki></jmol></nowiki>. If tags are not balanced, XML errors will occur).
<pre><jmol><jmolApplet><title>equatorial</title><color>white</color>
<size>200</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Pl506_14_equatorial.mol</uploadedFileContents></pre>
*Another example might be wish to indicate a citation using <nowiki><ref>...details </ref></nowiki> but in fact end up entering <nowiki><ref> ...</nowiki> (i.e. missing out the <nowiki></ref></nowiki>)
*If you do encounter such an error, try invoking your project as '''<nowiki>https://www.ch.ic.ac.uk/wiki/index.php?title=Mod:wzyz1234&action=history</nowiki>''' and edit and then save an uncorrupted version. You will need to be already logged in before you attempt to view the history in this way, since logging in '''after''' you invoke the above will return you not to the history, but to the corrupted page (Hint: it sometimes helps to check '''Remember my login on this computer''' as you log in). For example, the history for this page can be seen [https://www.ch.imperial.ac.uk/wiki/index.php?title=Mod:writeup&action=history here]. You can eg load this preceeding page, and then use it to replace '''writeup''' with your own project address.
*If the preceeding does not work try the instructions shown [[mod:fix|here]].

= Feedback =
Each Wiki page has a discussion section, including your submitted report page. 

See also: [[Mod:Cheatsheet|cheatsheet]]

Mod:gaussview

2015-10-07T16:42:59Z

Mjbear:

==About Gaussian (09) and GaussView (5) ==
Gaussian is a set of programs for carrying out electronic structure calculations. Many different methods for carrying out total energy calculations of molecules are implemented, including molecular mechanics (or force field) methods, but mainly semi-empirical and ab initio molecular orbital-based methods. In addition, energy derivatives as a function of inter-nuclear coordinates can be calculated, making it possible to optimise and characterise minima and transition structures on molecular potential energy surfaces. A basic outline of the electronic structure theory needed to work with the program is now given as part of the QM3 course.

For more information, see:

P. W. Atkins, J. de Paula, R. Friedman: Quanta, Matter and Change (Oxford University Press 2009)

F. Jensen: Introduction to Computational Chemistry (Wiley, 2007)

D. A. McQuarrie: Quantum Chemistry (University Science Books, 2008)

C. J. Cramer: Essentials of Computational Chemistry (Wiley, 2006)

==Learning to use GaussView==
Before you can run calculations on the various molecules you will be looking at, you will need to know how to submit them as "jobs" to Gaussian. The easiest way to do so is to use GaussView to create the molecule and tell Gaussian what to calculate and how.

=== Direct link to online Manual ===

Go [http://www.gaussian.com/g_tech/g_ur/l_keywords09.htm here] for an up to date explanation of all the keywords.


===Basics===
[[Image:Gaussview.JPG|right|500px|Initial GaussView Screen]]
Everything you need to make your molecular structure is available on the GaussView menu bar and it works primarily on a click and drag system. The first set of 11 icons from the left are what you need to create the desired structure. They are: 
'''Element Fragment''' - Brings up a periodic table for you to select an element and then it's structure and bonding. 
'''Ring Fragment''' - This allows you to quickly create common compound rings. 
'''R-Group Fragment''' - Gives easy access to common side chains. 
'''Biological Fragment''' - Gives a selection of Amino Acids and Nucleosides to add to your molecule. 
'''Custom Fragment''' - This allows you to save and load custom built structures. 
'''Modify Bond''' - Clicking on two atoms to create bonds of varing types and set the distance between atoms. 
'''Modify Angle''' - Clicking on three atoms allows you to specify the angle between them. 
'''Modify Dihedral''' - Clicking on four atoms allows you to specify the dihedral angle between them. 
'''Inquire''' - clicking two atoms shows you the distance between them, clicking three shows you the angle formed and clicking four shows you the dihedral angle formed. 
'''Add Valence''' - Adds a Hydrogen bond to the selected atom. 
'''Delete Atom''' - Deletes the selected atom.

Tutorial exercises are made available to you below. We suggest you work through these at your own pace. The GaussView tutorials assume you know where to find the relevant menus in GaussView. The Advanced tutorial should be taken after you have looked at the basic tutorial. If a section is proving very easy move onto the next one ...


[[mod:gv_basic | Basic GaussView Tutorial]]

[[mod:gv_advanced | Advanced GaussView Tutorial]]

The '''Help''' section is also very easy to follow. Click on the menu now to see what is available. As beginners the section on "GaussView Basics" and "Working with Molecules" are useful.

Work through as much as you need to - you may find you need to revisit the tutorials after attempting some of the exercises.

Mod:latebreak

2015-10-07T16:40:33Z

Mjbear:

= Late Breaking news 2013-2014 =
# March 13, 2014. Here is a [[Mod:g09#Combining_two_calculations_from_the_.fchk_files |neat trick]] for combining two separate checkpoint files (.fchk) into a single one. Most useful for combining the forward and reverse separate runs from an IRC calculation.
# 5 December, 2013. Two new methods for approximately predicting NMR spectrum have been identified. Compared to QM, these are ultra-quick.
## [http://chemapps.stolaf.edu/jmol/jsmol/testjsv_predict.htm based on on-line lockups]
## The Chemdoodle predictor via '''Spectrum/Generate'''.
# 2 Dec, 2013. A new option is available for building molecules in 3D (for use in energy minimisation programs such as Avogadro or ChemBio3D). Open ChemDoodle 6 and '''Structure>Clean>Build 3D Model''' - This function will generate 3D coordinates, adding hydrogens. Or '''Structure>Clean>Distance Geometry Embedding''' - This function is very useful for embedded systems, and will quickly estimate coordinates for structures like adamantane and fullerenes. You can rotate the resulting model in 3D using the '''Rotate in 3D button''' (3D cube with red arching arrow, fourth from the left). Export the coordinates in a 3D format (MDL molfile, CML) and import into eg Avogadro for further mechanics minimisation and preparation for Gaussian. ChemDoodle 6 will be deployed on desktop computers in a few days time. See me if you want it installed on laptops. --[[User:Rzepa|Rzepa]] 11:16, 2 December 2013 (UTC)
# 29 Nov, 2013. A new chemlab1 queue has been created. It uses only 1 processor and runs for a maximum of 1 hour. It should be used for any jobs that can complete within this time, and the purpose is to be able to publish the job to DSpace. Jobs run on a laptop cannot be so published.--[[User:Rzepa|Rzepa]] 14:31, 29 November 2013 (UTC)
# 25 Nov, 2013. '''MacBook Air and H: drives'''. Because the Air can take 2-15 seconds to establish a WiFi connection, it will have completed the login before it does. Under these circumstances, accessing your H: gives an error. To solve this, '''Finder/Go/Connect to server'''. Type smb://ic.ac.uk/homes/yourusername and '''+''' to remember it in your list of network drives. When you click on it, you should be prompted for your credentials. After this point, H: will become accessible.
# 15 Nov, 2013. Avogadro2 (for the QTAIM experiment) is now installed on all desktop computers in the two rooms. If you wish it to be installed on your laptop, contact Prof Rzepa. --[[User:Rzepa|Rzepa]] 11:01, 15 November 2013 (UTC)
# 15 Nov, 2013. Some clarification regarding which alkenes are to be epoxidised. The 1S experiment involves your epoxidising '''TWO''' available alkenes from a pool of four (using both catalysts), for which you should compute the NMR and rotation in the 1C experiment.
# 13 Nov, 2013. '''Avogadro:''' New versions have just been received from the developers, which may help with some of the stability issues. '''Avogadro2''' specifically appears much more stable regarding the QTAIM module, which it should be used for in preference to '''Avogadro1'''. The latter should be used for other operations. We will try to deploy these programs on a per user basis, so if you want to bring your laptop to me, I will install both programs for you. --[[User:Rzepa|Rzepa]] 07:01, 13 November 2013 (UTC)
# 21 Oct., 2013. People who obtain their internet from Virgin Media at home may have trouble connecting to the VPN. The fix for this is to log into your router's admin page, and then go to 'Advanced Settings', 'Firewall', tick the box to allow 'PPTP Passthrough', and then click save - you'll be able to log into the VPN after saving that change. Check [https://help.virginmedia.com/system/selfservice.controller?CMD=VIEW_ARTICLE&ARTICLE_ID=27550&CURRENT_CMD=SEARCH&CONFIGURATION=1001&PARTITION_ID=1&USERTYPE=1&LANGUAGE=en&COUNTY=us&VM_CUSTOMER_TYPE=Cable here] if you don't know how to access your router's admin page. --[[User:Pk1811|Philip Kent]] 23:35, 21 October 2013 (BST)
# 20 Oct.,2013. We have a new Wiki [[Mod:Cheatsheet|cheatsheet]] which has been tuned for us! Thanks Tristan!
# 18 Oct., 2013. All Desktop systems in the downstairs room have now been updated to the latest Java. The desktop computers upstairs will be updated over the coming weekend. The course laptops have also been updated. --[[User:Rzepa|Rzepa]] 12:11, 18 October 2013 (BST)
# 18 Oct., 2013. '''URGENT'''. Following on from the previous message, 8 Desktop computers in the downstairs computer room (along the south edge of the room) are now fully updated and can be used for Wiki editing as needed. More may be added later. --[[User:Rzepa|Rzepa]] 10:35, 18 October 2013 (BST)
# 18 Oct, 2013. '''URGENT'''. Some (all?) of you may have experienced an interesting time getting Java and Jmol to work yesterday. This was caused by the discovery by Oracle of urgent security issues in the version of Java installed on our systems, and hence an urgent need to upgrade. This can only be done by a system administrator, hence the pandemonium. Fortunately, in the last few minutes, a solution has been developed, and we hope to deploy it to as many systems as we can as quickly as we can. Laptops unfortunately can only be updated once they are returned to us. Watch this space for further news.--[[User:Rzepa|Rzepa]] 10:21, 18 October 2013 (BST)
# 15 Oct, 2013. Computing NMR spectra requires a reference TMS calculated at the same level to be inserted into the Gaussview program. This is done via a file [[File:Nmr.data|here]] which has to reside in the Gaussview folder, sub-directory '''data'''. Although all our desktop computers contain the latest version of this file, it is not been updated in the laptop builds. You should download this file and copy it into that folder (you should have admin privs for this operation)
# 14 Oct., 2013. The HPC job queues contain a mixture of short running jobs (< 30 minutes) along with one potential monster 37 hour effort. This last (the NMR spin-spin couplings for compounds '''18''' and '''17''') should be only used if you really feel it will help analyse your NMR; it should not be run ''just in case''. To help avoid building up a large backlog, clogged by a few 37-hour jobs, we have adjusted the maximum run time. Now the '''Gaussian 4px''' queue will only run for a maximum of 12 hours (which is more than enough time for all the calculations except the 37-hour monster) and the '''Gaussian 8px''' queue will run for 48 hours to allow the monster to complete. So submit all your jobs as 4px, and only run the monster if after careful consideration, you think it will help (for example, if no H-H couplings are reported in the literature, you would have nothing to compare to a calculation). The techniques described here are meant to be generic, and to be useful in other contexts, for example 3rd/4th year research projects. So just because it '''can be calculated''' does not mean it should be calculated.
# 12 Oct., 2013. A reminder that in order to simulate an experimental spectrum, the computed shifts and couplings have to be entered into a simulation program, such as '''gNMR''', available on all computers in the department. Be aware that it is limited in the total number of spins it can handle, probably about 10-12 only.
# 10 October, 2013. The [[Mod:organic#Procedure_for_Electronic_topology_.28QTAIM.29|QTAIM]] procedure in expt 1C requires Avogadro. Unfortunately, the Windows version of this program has a persistent and currently unresolved crashing bug. The Mac version of this program, as available on the iMac in the level 1 computer room does not (always) crash and hence this unit should be used for this part of the experiment. See also [[Mod:laptop#Using_a_MacBook_Laptop_for_the_Course|these instructions]] for how to use Mac Laptops. The Desktop Mac in the computer room is already network-wired and you can ignore those instructions.
## To get a screen grab of the QTAIM results, press the '''cmd''', '''shift''' (above the ctrl key) and '''4''' from the numerals at the top. This produces a cross-hair cursor, using which you should drag out the area you wish to capture. When you release this cursor, a screenshot is saved on your desktop, of type '''.png''' You can upload this file from the desktop into the Wiki.
## The latest version of Avogadro-1.1.1 for Mac can be found [http://avogadro.openmolecules.net/nightly/mac/unstable/ here].
## A non-crashing Windows version of Avogadro-1.1.1 is not yet available.
#8 Oct, 2013. [http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2013/press.html Nobel Prize in chemistry for computational modelling and simulation].
#6 Oct, 2013. We have made some tweaks during the summer to ensure that the default settings for '''G09W64''' are more appropriate for the resources available on laptops or desktops. In particular, the default memory allocation has been substantially increased, and the number of processors used by default is increased from 1 to 4. This should enable calculations to run (up to) four times as fast than they otherwise would have done. If you observe that what is asserted here is not in fact the case, please contact me. [[User:Rzepa|Rzepa]] 09:02, 7 October 2013 (BST)

= Late Breaking news 2012-2013 =

# CRC handbook error. The CRC handbook 93rd edition has an error in it, section 9, page 107, for the stated Thallium - Bromine bond length. The editor-in-chief has been contacted and a correct value of the first digit (before the decimal) was confirmed to be 2, '''not''' 1 as stated in the book. --[[User:Jrc10|Jrc10]] 11:14, 18 January 2013 (UTC)
# Freezing Coordinates. [[File:Freeze-coordinate.jpg|right|thumb]] Finding a transition state can involve specifying a bond as frozen, using the Redundant coordinate editor. Because of a change introduced in Gaussian 09, revision C.01, if you try to set a value for the bond in the editor as shown to the right, when the Gaussian program runs it will ignore this specification completely (resulting in no bond being frozen). So do not use this feature of the redundant coordinate editor.--[[User:Rzepa|Rzepa]] 14:49, 3 December 2012 (UTC)
# Referencing a published calculation [[File:Full-publish.jpg|right|300px]]
You are asked to '''publish''' the key calculations you run on the HPC-SCAN system. When you do so successfully, the result will include a field that looks like this:
<pre>dc.identifier.uri http://hdl.handle.net/10042/21671</pre>
To quote this result in your wiki, insert this component: '''<nowiki>{{DOI|10042/21671}}</nowiki>''' with the result: <ref name="10042/21671">{{DOI|10042/21671}}</ref>.
You are using the same system which is normally used to reference scientific publications, but here in the context of a scientific calculation. If you are interested, the full features are shown on the right, and can be set by editing your HPC-SCAN profile. '''ChemPound''' is another local repository, and '''Figshare''' is an open resource repository which also issues you with a quotable DOI. To publish there however you will need to obtain a Figshare key and secret. The FOAF entry is a so-called RDF declaration, which enables you to identify your credentials for use on the Semantic Web.--[[User:Rzepa|Rzepa]] 08:46, 17 November 2012 (UTC)
<references />
# The WikED editor. As originally envisaged, the [http://en.wikipedia.org/wiki/User:Cacycle/wikEd WikEd] editor supported Google Chrome, FireFox and Safari. As of 2012 however, the latest Chrome appears to no longer support this editor toolbar. Internet Explorer never has. If you want to take advantage of this editor, please use FireFox only (or Safari on a Mac). There is also [http://www.mediawiki.org/wiki/VisualEditor another project] to improve visual editing, with an expected first release in December 2012.
# Using an iPad or iPhone for the course. Much of the course is web browser based. But recently, one can also access the file system to inspect output (.log) files for errors etc. You need to install a (free) app called [https://itunes.apple.com/gb/app/mobilecho/id429704844?mt=8 Mobilecho] and configure it as shown [http://www2.imperial.ac.uk/blog/ictfaq/2012/10/26/configuring-mobilecho-on-your-ios-device/ here]. This allows you to '''preview''' files stored in your H: drive (remember to store them there using your laptop or desktop). I have not yet found any IOS app capable of actually viewing the output as a graphically represented molecule, but that may come soon.
Another (this time not free, £2.49) app which might be useful is [https://itunes.apple.com/gb/app/wiki-edit/id391012741?mt=8 Wiki-edit], which allows a Wiki to be edited using an iPad.
If anyone discovers functionality for an iPad other than browser and preview based, do let me know. --[[User:Rzepa|Rzepa]] 15:21, 8 November 2012 (UTC)
# Avogadro. I an looking for volunteers to try out [[Mod:avogadro|Avogadro]] as a replacement for ChemBio3D. The latest version of the program is installed on all laptops and desktops, and its operation is reasonably intuitive. It can serve as a base for performing molecular mechanics '''pre-minimisation''' (tidying) of coordinates, and can export these coordinates to other programs such as Gaussian for further analysis.
If you do try to use it, please document your experiences [[Talk:Mod:avogadro|here]]. --[[User:Rzepa|Rzepa]] 11:20, 7 November 2012 (UTC)
# Working with laptops at home. [[File:Gpupdate.jpg|right]]The initial attempt to square the circle by allowing you to open/save files in your H: drive whilst working at home was sub-optimal, with spinning cursor freezes occurring frequently. ICT has taken a close look at the so-called policies configured into the laptop and come up with what is hoped will be a more responsive configuration. To implement this new policy, you have to do the following whilst using the laptop in College (or with the VPN on at home). Type into the search box invoked from the start menu '''gpupdate /force '''. This will take around 2-4 minutes. You will need to log out and then in again to complete the process. It is also not unusual to experience spinning cursor delays whilst working in the study area on level 2. This in part is a result of our having to move the location of the laboratory at a late stage into one where the Wireless base station had insufficient capacity. We hope however that a new base station will be fitted very soon which should improve matters in this regard. --[[User:Rzepa|Rzepa]] 12:48, 23 October 2012 (BST)
# SCAN job queues. [[File:Chemlabq.jpg|right|200px|Chemlab 1 job queues]]A new job queue has been added. This uses 8-processors in parallel to run a job, whereas the normal queue uses only 4. Please use this new queue for computing larger molecules.
# Uploading cub files to create rotatable surfaces on the Wiki. The [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:writeup#Incorporating_Orbital.2Felectrostatic_potential_isosurfaces_into_a_Wiki instructions here] describe how you can create a '''cub''' file using Gaussview, convert it to a highly compressed format known as '''.jvxl''' and upload that to your Wiki. We have established that the cub file ''must not'' be in your (network) H: drive if you are using a Windows computer. To be able to upload these files, go to '''Computer''' and then drive C:\temp and put all your cub files into the '''hard drive''' of the laptop directly. They can then be [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ converted using this link] into .jvxl files.
#Poor laptop performance at home. There has been a ''perfect storm'' of three changes made over the summer: an increase in student H: drive storage quota, procurement of new laptops and a change in ''appdata policies''. It seems that these interact, producing undesirable effects on the laptops when they are taken out of the Campus environment. The new appdata policies in particular seem to be at the centre of things. This means that any application that writes temporary or permanent files now does so to the users H: drive instead of as previously to the local C: drive of the device. This also includes the ''desktop'', in other words any document saved to the desktop is now saved on H: rather than C: (the aim being to ensure that the document is always available to you no matter what machine you sit down in front of). This scheme works well when the laptop is connected to a high bandwidth network, but may not perform so well in a domestic environment. I have asked ICT to look at optimising their policies for laptops so that some of the issues many of you have experienced may be either entirely removed, or at least substantially reduced. These new policies are likely to be tested on Wed 17th October by myself using a standard issue laptop. I will report back here what I discover. So hang on in there! --[[User:Rzepa|Rzepa]] 10:57, 15 October 2012 (BST)
# VPN connections and working at home. A number of people have reported that the VNP (virtual private network) connection (a shortcut for which is on the laptop desktop) does not work. I have taken a "vanilla" laptop home and tried to see what happens:
#*I firstly connected the laptop via an ethernet cable to the Wireless/Broadband router. A network is detected automatically by Windows and configured appropriately.
#With a network up, clicking on the VPN desktop icon throws up a prompt to enter the user name, password and domain (the value for the latter should be '''IC'''). This worked without problem.
#* This allows one to e.g. connect to journals and download articles etc (this would not be possible without the VPN working properly)
#* Note that you '''do not need''' the VPN on to log into the Wiki to edit your pages there.
#* You '''DO''' need the vPN on to connect to https://scanweb.cc.imperial.ac.uk/uportal2/
#I then pulled the ethernet cable out and used the WiFi connection instead (Control panels/Network and sharing Center), connecting to the SSID of my WiFi router and supplying the security password. ICVPN again connected with no problem, and again I was able to download journal articles, and save into my H: drive. So what might be going wrong that disables the VPN access? Well, one possibility is that the ISP you are signed up with does not support something called '''VPN Pass-through'''. VPN is often considered a ''business feature'' and many domestic ISP providers have VPN disabled (perhaps as an encouragement for you to sign up with a more expensive business package). Lack of VPN is also often seen with so-called Free WiFi services (often found in hotels and public areas), again possibly to encourage you to sign up for paid-for deals. So the first thing to check would be whether your ISP does actually support VPN. Quite what else might be going wrong would only be speculation on my part. But the bottom line is that the laptops provided for the course ARE capable of VPN connection without any tinkering.--[[User:Rzepa|Rzepa]] 18:01, 11 October 2012 (BST)
# Offline H drive. The default setup for undergraduates this year is that the desktop and appdata folders are redirected to the H drive. This can cause mystification for laptop users when the machine is offline. Desktop icons vanish. H:\appdata contains settings for Firefox and other programs and things stop working as expected.
To make things a little easier we have enabled caching for the H drive, so it will be available offline. It will synchronise automatically when you are connected to the college network. Do note that it will also synchronise if you are connected via the VPN and if you are on a capped broadband contract you should bear this in mind. - Nick
# Firefox, Java and the Wiki. [[File:Java-1.jpg|right|thumb|Activating Java 1]]Firefox needs Java enabled to run the Jmol applet, which displays molecules, vibrations, MOs etc. The setting which determines this is user specific (it is stored in a file in your H: drive). If you are not getting molecules, but instead a yellow box telling you no Java is enabled, proceed as follows:
#In the menus at the top of FireFox, '''Tools/Add-ons/Plugins'''.
# Scroll down to ''Java(TM) Platform SE 6 U31 6.0.310.5'' and activate it. The security message which indicates that the Java is out of date should be ignored for the time being.
# Refresh the Wiki page (or restart the browser). You should get a pop up box which reads ''The applications digital signature cannot be verified. Run''
# This indicates that Java is now active again. Run the applet and your molecules should now appear.
# Publishing to DSpace. [[File:Publish-2-dspace.jpg|right|300px]]The instructions suggest that you publish select jobs to Dspace. There is current a ''bug'' in the profile which prevents this until you have actually activated the publish as shown on the right. [https://scanweb.cc.imperial.ac.uk/uportal2/ Login] to the SCAN HPC service and select '''Profile''' from the list on the left. Check the button showing '''Publish to Dspace''' (it should have been on by default, but in fact its off. Apologies. We hope to fix this shortly).
#Also, the publish command needs sometimes to "wake up" the DSpace server. It may not do this the first time you try to publish, but it normally works the second time.
#If the job cannot publish, the chances are that there is an error in the job that prevented the writing out of the publication files. You will need to open the job output using Notepad++ (Right-click on the file and select NotePad++ or other text editor such as WordPad) and see what the errors are at the bottom of this file. You may need to discuss these with a demonstrator to determine what went wrong.
# Versions of Gaussian. The laptops contain both G03W and G09W 64-bit. Unfortunately, only the first of these is recognised by ChemBio3D V 12. So if you try to run Gaussian from ChemBio3D, it will run G03W. A new release of ChemBio3D V 13 came out over the summer, but try as we might, we cannot get the global licensing codes to reliably work. As an interim measure therefore, we have reverted back to ChemBio3D V12 on your install. However, you can download V13 yourselves for installation on a computer from [http://scistore.cambridgesoft.com/sitelicense.cfm?sid=948 this site] and this will give you a licensing code specific to you which you can use (with only three attempts allowed) to install and license the newer version. G09W contains many updated features, but you would normally be expected to make use of many of them. Perhaps the only significant difference from your point of view is that you can allocate more memory to run Gaussian using the %mem=2GB command. This should make it run (somewhat) faster.--[[User:Rzepa|Rzepa]] 10:56, 5 October 2012 (BST)
= Late Breaking news 2011-2012 =
== Incorporating Orbital surfaces into a Wiki ==
The procedure is as follows
# Run a Gaussian calculation on the SCAN
# When complete, select ''Formatted checkpoint file'' from the output files and download
# Double click on the file to load into Gaussview
# '''Edit/MOs''' and select (= yellow) your required orbitals.
# '''Visualise''' and '''Update''' to generate them
# '''Results/surfaces/contours''' and from the '''cubes available''' list, select one and '''Cube actions/save cube'''
# Invoke [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ this page] and you will be asked to select your cube file,
# followed by three file save dialogs, one for the coordinates (.xyz), one for the MO surface (.jvxl) and a package (.jmol).
# Insert the following code into your Wiki, replacing the file name with your own choice from the preceding file save dialogs (the string ''images/4/42/AHB_mo22.jvxl'' is for illustrative purposes only and must be edited as described below).
<pre><nowiki><jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol></nowiki>
</pre>
# [[image:absolute_path.jpg|right|350px]]Next, upload the the .xyz and .jvxl files into the Wiki (one file at a time, the multiple file uploader does not seem to work for this task)
## You will need to find the absolute path for the .jvxl file. Above, this appears as '''images/4/42/'''AHB_mo22.jvxl
## Just after uploading the .jvxl file, you will see a response as shown on the right.
## Right click on the link (blue arrow) and select '''Copy file location''' (this can be browser specific)
#Paste this string into the above, and edit it down to just '''images/4/42/AHB_mo22.jvxl''' (ie trim <nowiki>https://wiki.ch.ic.ac.uk/wiki/</nowiki> off if that is how it appears)
#You should get something akin to:
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;
</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
* You can superimpose two surfaces. Change the script contents above to <pre>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;isosurface append color red blue "images/4/42/AHB_mo23.jvxl" translucent;</pre>
* The four colours used in this line can be changed to whatever you consider appropriate.
=== An alternative simpler way of loading surfaces ===
This method avoids the need to specify paths to files as seen above. Instead it uses the '''.jmol''' file (as a zip archive) which contains all necessary information and can be invoked by
<pre><nowiki><jmolFile text="just a link">AHB_mo22.cub.jmol</jmolFile></nowiki></pre> which produces <jmolFile text="just a link">AHB_mo22.cub.jmol</jmolFile>. The disadvantage is that it only supports one surface (you cannot superimpose two orbitals). --[[User:Rzepa|Rzepa]] 07:35, 6 March 2012 (UTC)

== Report discussion ==

A reminder that if your report shows a Blue link (rather than red) at the top, you will find some comments on it, which we make during the marking of the report. This is separate feedback to your grade, which is being processed via the Blackboard system, and may appear a day or so after the discussion. So for instant feedback, look at the discussion.--[[User:Rzepa|Rzepa]] 09:51, 1 February 2012 (UTC)

== Crystal structure files as initial 3D coordinates for modelling ==

The start point for obtaining 3D coordinates can be
# ChemDraw via its templates feature, which has a wide selection of small molecules, used as an alternative to sketching the molecule from scratch.
# The [http://www.molecular-networks.com/online_demos/corina_demo.html Corina tool], which can be used to create a Molfile of coordinates from a SMILES string generated using ChemDraw.
# The Conquest interface to the Cambridge crystal structure database.
## Invoke this by typing Conquest into the search box produced by invoking the Windows tool on the bottom left.
## When a search is completed, invoke '''export''' and '''Mol2''' as the format. Select current entry, one file per entry and save (to desktop).
# This file should now be readable using ChemBio3D.--[[User:Rzepa|Rzepa]] 12:45, 20 January 2012 (UTC)

== Multiple File uploads ==

At special request, a multi-file upload facility has been added on an experimental basis. The link appears in the sidebar on the left. Please try out and report any problems --[[User:Rzepa|Rzepa]] 13:48, 27 October 2011 (BST)

== DSpace depositions ==

If you have tried to publish a calculation into Dspace recently, it will have failed. This in part is a knock-on effect from the power outage this last weekend, the full implications of which took several days to sort out. As of this instant, publication is working again. If you have something you tried to publish yesterday (Monday) send the portal Job ID to Mat Harvey (m.j.harvey@imperial.ac.uk) and he will correct the entry.--[[User:Rzepa|Rzepa]] 11:25, 18 October 2011 (BST)

==Improvements to the Editing interface ==

An enhanced editing toolbar called WikEd is now installed for all users and most browsers. You should spend a little while exploring its features.

== ChemBio3D version 12 ==

Version 12 (and 11) of this program contain several errors/bugs. The vendors were informed of these more than two years ago. Unfortunately, it seems as if V13 of the program will not be released in time to be used on this course. So you will have to watch out for the bugs.

= Late Breaking news 2010-2011 =

== Another way of fixing a broken page ==
Try this [[Mod:fix|method]] if the revision history method fails. This is based on trying to back up your project (errors and all) to an editable file,
and then re-editing the file to remove any error that you manange to spot. --[[User:Rzepa|Rzepa]] 21:35, 24 February 2011 (UTC)

== Laptop shutdowns at 22.20 ==

Not too many people are actively using their laptop at 22.30, but what has emerged is that routine maintenance procedures are hard-coded (Crontab) into the software build to reboot the system at this time every day. The maintenance involves applying new security patches, new virus definitions, new software releases etc. If your laptop is online just before 22.30, you may notice this activity. Windows 7 then invariably requires the system to be rebooted for the patches to take effect. This will happen irrespective of whether any software patches have been applied. So, at around 22.15 or so, it is essential that you save all work. If you do not, it may be lost when the system reboots. --[[User:Rzepa|Rzepa]] 13:01, 21 February 2011 (UTC)

== Mini Project ==

During the course of grading the project, I discovered some people did have time to do calculations, but the ran out of time for the write up of the project. If you are in such an unfortunate position, do at least put the DOI of the published calculation into your report (this takes just a few seconds). That way, you can at least get some credit for having selected a molecule and calculated it, even if you do not have time to discuss your results on the project page. As with the Wiki report, the DOI entry is also time stamped, so we can easily verify that the calculation was done before the deadline! --[[User:Rzepa|Rzepa]] 09:32, 1 February 2011 (UTC)

== Why Wiki ==

A question occasionally asked is why the course report uses a Wiki instead of the more familiar (to most people) Microsoft word format. Some of the reasons why are [[Mod:writeup#Why_Wiki.3F |summarised here]].

== Plagiarism ==

We have implemented strong plagiarism detectors for submitted reports. This would include detecting similarities with previously submitted reports. You should be reminded that plagiarism is taken very seriously indeed, and any detected will have serious consequences for the plagiariser.

== Converters for Wiki ==

It was there, but it got lost (honestly!). See [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:writeup#Converters_to_the_Wiki_format: here] for some hints on how to convert other formats (Word, HTML) to the Wiki format.

== '''Prettifying Plots produced by Gaussview.'''==
GV (5.09) can visualise spectra (NMR, IT, etc), as well as SCANs and other properties. However, the resulting graphs are not very suitable for inclusion, since the default text sizes are too small, the lines may be very thin and the units for the labels unhelpful. To tweak these spectra, proceed as follows:
# Use Gaussview, and select '''Results/vibrations''' or '''NMR/Scan/UV-Vis''' etc.
# Right mouse click and select '''properties'''. Here you can select more sensible units, and also the origin.
# Right mouse click and select '''Export'''. Save the (.svg) file (SVG is to images what HTML is to text).
# Using Wordpad (or other text editor), open up the .svg file
# Near the top, you will see e.g. the text '''Scan of Total Energy'''. Replace by what you want.
# You will see '''font-size:14;''' Change to something larger.
# Further down, you will see '''font-size:10;''' Change to something larger.
# You will see lots of '''stroke-dasharray:3;''' Delete them all (a global replace).
# You will see a line starting '''polyline'''. It contains '''stroke-width:0.9;''' Change to something like '''stroke-width:2.7;'''
# You will see a line starting '''rect'''. It contains '''rgb(255,255,245);''' Change this to '''rgb(255,255,255);'''
# Save the edits, and drop the .svg file onto a FireFox browser Window. The spectrum should appear. If you make further changes, refresh the browser window to see them.
# At this point, you probably want to take a screen-grab of the browser window (as a .gif or .jpg file). Upload this to the wiki to incorporate into your report.

== Module 2: VPN for home use ==
Due to the wiki server being hacked it has been brought in behind the college fire-wall. If you want to access it from home (or the scan servers), you must first connect via VPN. If you don't the wiki will not load.

== Module 1: Errors in log file ==
When running SCAN calculations, if no Checkpoint file is produced, or other errors occur, its best to inspect the Gaussian log file using '''Wordpad'''. The errors will be seen at the bottom of this file. However, the default font size for Wordpad is 11, which causes the output in the log file to wrap around, causing it to become unreadable. So before you try to inspect this output, set the font size to '''9'''. This produces much more readable outputs.

== Module 1: Iodine containing molecules ==
Although the Mini project is designed to be based on organic molecules, occasionally other elements creep in. One such is iodine, which causes problems because the 6-31G basis set is not available for it. In such circumstances, you can always go to [https://bse.pnl.gov/bse/portal the basis set exchange] to get one. A (partial) example of its use is shown below, in which the built in basis is used for C, but the basis set exchange one for I (in fact the 6-311G basis):
<pre># rb3lyp/gen opt

General basis set, including that for iodine

0 1
I -0.58031145 -1.18849341 0.11015250
C 0.73981873 1.76844662 -0.08747886
....

C H etc 0
6-31G(d,p)
****
I 0
S 5 1.00
444750.0000000 0.0008900
66127.0000000 0.0069400
14815.0000000 0.0360900
....
****</pre>

= Late Breaking news 2009-10 =

== Module 1: Project FAQ ==

Because the project is defined not in the scripts but by you, it can sometimes seem rather open-ended. So, after an interesting chat with one student, I came up with three possible objectives you could set yourself for the project.

# The most ambitious is that you spot a structure in the literature which seems to ring alarm bells. Can it really be that, you ask yourself. Well, if 13C and other spectroscopic data has been reported, you can calculate it and see how well it matches. You might conclude that either its a good match, or not.
# A follow up to the first category, is that if the match is poor, you suggest a better one. this is HARD. We do not expect that of you!
# More common is that two possible structures have been reported, and you might wish to check that they have been assigned correctly and not transposed.
# Another scenario is that the 13C for any given structure is simply reported as a series of values, with no attempt to assign each peak to a specific carbon in the compound. By calculating the spectrum, you can make this assignment.

Any one of the four above is a reasonable objective to set yourself in this project.--[[User:Rzepa|Rzepa]] 15:38, 25 January 2010 (UTC)

== Anti-Bredt Natural products? ==

The [http://totallysynthetic.com/blog/?p=2236 blogosphere] is buzzing discussing a natural product reported in {{DOI|10.1016/j.bmcl.2009.10.016}} which contains a bridgehead alkene in a small ring. The 13C data is difficult to get from the article, but the structure is an interesting one to analyze using the techniques we show you here. Some of the blogs also are commenting on the early modelling efforts A nice breaking news story that you might wish to look at! (the result of all this attention is a corrigendum, DOI: {{DOI|10.1016/j.bmcl.2010.04.003}}). And [http://pubs.acs.org/isubscribe/journals/cen/88/i02/html/8802news3.html how about this] (update: This too has been retracted).

== NBO of BH3 has the sAO as the "lone pair" ==
Something is wrong! The likely problem is that you don't have the ground state lowest energy electronic structure. If you computed the B3LYP/3-21G geometry and then used B3LYP/6-31G to compute the population, the system is not optimised at the B3LYP/6-31G level and your answer will be wrong. Excellent if you noticed this discrepancy. Compute the population analysis and NBO with the 3-21G basis set and you should get a correct analysis. If not, check the energy of your calculation does it give -26.4622632920?

Alternatively if you used the 3-21G basis set ... the new version of G09 prints the NBO analysis slightly differently, the nbo web-page has now been updated to reflect this and explains in detail where to find the correct pz AO.

Could someone perhaps pose the question, to which we see an answer here? --[[User:Rzepa|Rzepa]] 07:32, 20 January 2010 (UTC)

== Displaying Vibrations ==

[[Image:jmolvib.jpg|thumb|right]]The write-up section of the course describes how you might animate a vibration using the Wiki. Unfortunately, our upgrade to Gaussian 09 brings with it changes to the manner in which the vibrational information is written out, which Jmol cannot understand. The result is an error message rather than a vibration. I have contact Bob Hanson, editor-in-chief of Jmol and no doubt a fix will be sorted out shortly. --[[User:Rzepa|Rzepa]] 13:09, 16 November 2009 (UTC)

'''UPDATE:''' The problem noted above is now fixed. If you take a look at [[Mod:writeup#Enhancing_your_report_with__Jmol_models_and_Vibrations|this entry]] you will see Jmol reading a Gaussian 09 vibration log file and displaying a vibration. This new version of Jmol offers other new features. If you right-mouse-click, a menu appears. The top item of this is the data model. This will contain all the optimisation steps in the log file, together with all the vibrational modes identified. Any one of these can be selected for display.--[[User:Rzepa|Rzepa]] 08:30, 17 November 2009 (UTC)

== Backing up your report ==
[[Image:export1.jpg|left|250px]][[Image:Export2.jpg|right|200px]]Invoke [[Special:Export|this utility]] to back your project up. In the box provided, enter e.g. '''Mod:wzyz1234''' being the password for your report. This will generate a page (right) which can be saved using the Firefox '''File/Save_Page_as''' menu. Specify '''Web Page, XML only''' as the format, and add .xml to the file suffix. You might want to do this eg on a daily basis to secure against corruption. This is in addition to the notes for how to repair broken pages.

The same file can now be reloaded using [[Special:Import|Import]].

== Using the LANL2DZ Pseudopotential Basis set ==

We have reports that using the keyword '''b3lyp/lanl2dz''' for elements such as Al and Cl produces an error-free log file, but no .fchk file is produced. This is because the conversion program that converts the initially produced .chk file to .fchk (a process needed because the .chk file is specific to the type of computer the calculation was run on, and will not work on Windows computers) is failing to covert the file. We think this is probably an error in the way Gaussian09 produces that .chk file rather than a failure of the converter (the error has been reported to Gaussian for clarification).

One option is to take the optimised geometry and carry out a single point calculation with a full basis set, for example 6-31G(d) which is the same as 6-31G* (just different notation) and then use the checkpoint from this job to visualise the MOs.

Another alternative is to use the following keywords: '''b3lyp/Gen read=pseudo''' and then after the blank line that terminates the geometry, to read in the basis set and pseudopotential. These can be obtained from [https://bse.pnl.gov/bse/portal the Basis set exchange]. Select all the elements present in your molecule from the Periodic table display, and from the left, select the '''Orbitals with effective core potential''' pull down. Then scroll to '''LANL2DZ ECP''', select as the format '''Gaussian94''' and press '''Get basis set'''. A Window appears, and you should select all the content in that Window and paste it into your Job input file (using eg Wordpad) after the geometry blank line. One further edit is needed. The section in the basis starting <pre>! Elements ...</pre> is terminated by two blank lines. Delete '''one''' of these blank lines (leave the other). The result should look something like this (only Al is shown in part, the other elements are not shown for brevity).
<pre>
H 3.33099000 -2.03083200 -0.89612200
H 1.96515000 -2.65853800 0.03207800

Al 0
S 2 1.00
0.9615000 -0.5021546
0.1819000 1.2342547
S 1 1.00
0.0657000 1.0000000
P 2 1.00
1.9280000 -0.0712584
0.2013000 1.0162966
P 1 1.00
0.0580000 1.0000000
****
! Elements References
! -------- ----------
! Na - Hg: P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 270 (1985).
! P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 284 (1985).
! P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 299 (1985).
!

AL 0
AL-ECP 2 10
d potential
5
1 304.7291926 -10.0000000
2 61.5299768 -63.8079837
</pre>

The advantage of the general basis set is that a very much wider selection of basis sets is available (Gaussian only has a sub-set of these built in), including many of the most modern.--[[User:Rzepa|Rzepa]] 09:40, 30 October 2009 (UTC)

== Slow Running of laptops ==

We have had some reports of slow response using Gaussview. This has been identified as having too many programs open simultaneously. This is a generic problem, which we suspect most people experience at some stage in their use of computers. It does not appear to be connected to this lab course in particular. Before you conclude your laptop is malfunctioning, try closing down all the programs except Gaussview and see if it makes a difference.

== Associating FireFox with Gaussview 5 not 3 ==

Gausview 5 was received very late by us (late September 2009), and has not been subjected to full testing. We installed it for compatibility with Gaussian 09, and some properties (Vibrations) need GV5 to display properly. Currently, when FireFox is used to inspect Gaussian 09 computed vibrations, it starts up GV3 rather than 5. To reconfigure the browser for GV5, proceed as follows:
# In the Tools/Options menu, select ''Applications''
#Find the entry for '''OUT file''' and Click on the associated action
# Set it to ''always ask''
# Now a prompt appears on downloading a Logfile, so browse to gauss.exe (in Program files/GV5) and check ''do this automatically from now on''.
#This should ensure that GV5 rather than GV3 is invoked automatically.

== Queue status ==

Some people have queried how the queues work. Below is a brief explanation made to those students in an email. It might help you understand what is going on ''under the hood''.

''The queues do seem normal in most respects. As of 16.00 there were 16 jobs running in chemlab1 (the max) and 19 pending. By about 20.00 the number of pending jobs were down to 3. This morning at 07.00, only 3 jobs remained in the queues, none pending. This is pretty much what one expects. Chemlab2 on the other hand has all machines still claimed as of this morning. I am checking out if this is simply a full queue, or a hung queue! If the job on this queue does not complete by 7.30, it is stopped (so that the machines can boot back to windows) and an attempt to run it again next night is made. If the job cannot complete in 10 hours (because the molecule is big, ie more than about 20 nonhydrogen atoms), it will only run to completion on weekends, or on chemlab1. This is why the instructions suggest using maxcycles=25 (or less). This limits the job and allows it to complete overnight.''

''Very much part of this lab is learning to manage your resources. It might be a steep learning curve, but it is also very much what the real research world is about! Fortunately, Moore's law does mean that you get more bang for buck each year. Thus for both vibrations and 13C, Gaussian 09 is about twice as fast as what we had last year! But do remember that the time scales as N**4 (N= number of atoms). So only a few methyl groups extra can double the calculation time! ''

''If individual jobs fail with no output, this probably indicates either a problem with an individual user's account (Matt Harvey will tell us), or that the input is too defective to produce any. In this latter category, do spread the word to come to my office and I will perform a triage on this before escalating to Matt. '' --[[User:Rzepa|Rzepa]] 07:20, 22 October 2009 (BST)

==Remote connections and use of Gaussview on non College Computers ==
[[image:rdc.jpg|right|thumb|RDC connection]]With laptop hand-back not fully overlapping with write-up deadlines, a number of people have asked how they might be able to access the course programs without the need to physically be present in the two computer rooms. The Gaussview license in particular does not allow installation on non-Imperial computers. To overcome this restriction, you can do the following:
#Use Remote Desktop Connection, which is installed on most Windows computers.
#Establish a VPN connection if you are off-campus
#Connect to '''chas.ch.ic.ac.uk''' (the chemistry application server). You will be presented with the same screen as you would if you were physically at the computer. This includes all the software etc.
#You will find that some operations are more stodgy than others (surface rendering for example) but if you have a reasonably fast (i.e. broadband) connection, the experience is not too bad.##You can test the above (but without the need to set up the VPN) from one of the static computers in the computer rooms.--[[User:Rzepa|Rzepa]] 12:55, 18 December 2008 (UTC)

== Conversion of Word to Wiki format==
If you prefer to author your report using Word, and then at the final stage convert it to the Wiki, you can do so using OpenOffice 3.0. This has a Word to MediaWiki converter which allows you to save the file in Wiki text. This can then simply be pasted into your Wiki page. It might need some tidying up (in particular, Jmol molecules can only be added at the wiki stage, and not so in Word itself), and you will have to still upload the graphics in the Wiki. Since Januar 2009, V 3.0 of openoffice has been installed which supports this feature.--[[User:Rzepa|Rzepa]] 17:05, 23 January 2009 (UTC)
#Several people have reported that Word is crashing during use. We think it might be because you have used it to open a document located on the network drive H:. If your network goes down (see above) whilst you are editing the document, Word may well panic and hence crash! To avoid this, and whilst you still have a network, make a copy of any Word document from drive H: to the hard drive E:. Then, only ever edit that local copy. Finally, when you are finished, copy the document back from E: to H:. Hopefully, this will avoid any Word crashes.--[[User:Rzepa|Rzepa]] 10:37, 17 October 2008 (BST)
==Email Alerts ==
You can receive email alerts if any page on the wiki is changed (ie when additions to this page are made). Click on the '''watch''' link at the top of any page and then on the '''my preferences''' link (you have to be logged in), tick the '''E-mail me when a page I'm watching is changed''' box.

----

Mod:writeup

2015-10-07T16:36:01Z

Mjbear:

See also: [[Mod:Cheatsheet|Cheatsheet]].

== The expected length of the report ==
A Wiki does not have pages as such. But as a very rough guide, expect to produce something the equivalent of about six printed pages (although you can invoke ''pop-ups'' and the like which make a page count only very approximate). Use graphics reasonably sparingly, and to the point.

= Why Wiki? =
Since everyone is used to using [http://www.wordonwiki.com Microsoft Word], why do we [[talks:rzepa2011|use a Wiki]] for this course? Well, the Wiki format has several advantages.
#A full revision and fully dated history across sessions is kept (Word only keeps this during a session). This is more suited for laboratory work, where you indeed might need to go back to a particular day and experiment to check your notes.
#The (chemistry) Wiki allows you to include molecule coordinates, vibrations and MO surfaces which can be rotated and inspected, along with other chemical extensions. Word does not offer this.
#The Wiki allows you to include "zoomable" graphics in the form of SVG (which Gaussview generates), and access to the 17-million large [http://commons.wikimedia.org/wiki/Main_Page WikiCommons] image library, as well as access to the Wikipedia InterWiki.
#The [[w::Help:Template|template]] concept allows pre-formated entry. There are lots of powerful [[w:Category:Chemical_element_symbol_templates|chemical templates]] available.
#Autonumbered referencing, and particularly cross-referencing, is actually easier than using Word.
#You (and the graders) can access your report anywhere online, it is not held on a local hard drive which you may not have immediate access to.
#It has automatic date and identity stamps for ALL components, which means we can assess that part of the report handed in by any deadline, and deal separately with anything which has a date-stamp past a given deadline. A Word document has only a single date-and-time stamp and so deadlines must apply to the whole document.
#And we have been using Wikis for course work since '''2006''', so there is lots of expertise around!
#And finally, Wiki is an example of a [http://en.wikipedia.org/wiki/Markdown MarkDown] language, one designed to facilitate writing using an easy-to-read, easy-to-write plain text format (with the option of converting it to structurally valid XHTML).

=Report Preparation =

== Before you start writing ==
Before you start writing, you might wish to read this article<ref name="adma.200400767">G.M. Whitesides, "Whitesides' Group: Writing a Paper", ''Advanced Materials'', '''2004''', ''16'', 1375–137 {{DOI|10.1002/adma.200400767}}</ref> (or perchance this advice<ref name="ac2000169">R. Murray, "Skillful writing of an awful research paper", ''Anal. Chem.'', '''2011''', ''83'', 633. {{DOI|10.1021/ac2000169}}</ref>). In your report you should discuss your evaluation of each of the techniques you use here. You should include at least '''three literature references in addition to the ones given here'''. You might also want to check the [[Mod:latebreak|late breaking news]] to see if there are any helpful hints about the project you might want to refer to. You will be writing your report in Wiki format, and it is best to do this continually as you do the experiment. In effect, your Wiki report is also your laboratory manual.

#[[File:Wiked.jpg|right|400px|WikED editor]]Open Firefox as a Web browser.
#There should be a tab for the course Wiki, but if not, use the URL '''www.ch.ic.ac.uk'''
#*[[Image:exception1.jpg|right|thumb|Security exception]]If the browser asks you to add a security exception, do so and proceed to '''view/confirm''' the certificate.
#You can view the Wiki without logging in, but to create a report, you will have to login as yourself. Check '''Remember my login on this computer'''
#Before you start, you might want to visit the [[Special:Preferences|preferences]] page to customise the Wiki for yourself.
#Follow the procedures below. Check that the WikED icon is present at the top, just to the right of the log out text (ringed in red). If you want a minimalist editing interface, click this icon to switch it off. A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.

=== Assigning your report an identifier ===
#*[[Image:New_report.jpg|right|400px|Creating a report page]] In the address box, type something like
#**'''wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:{{fontcolor1|yellow|black|XYZ1234}}'''
#*The characters '''Mod''' indicate a report associated with the modelling course, and '''{{fontcolor1|yellow|black|XYZ1234}}''' is your secret password for the report. It can be any length, but do not make it too long! It should then tell you there is no text in this page. If not, try another more unique password. You should now click on the '''edit this page''' link to start. Use a different address for each module of the course you are submitting.
#*It is a {{fontcolor1|yellow|black|good idea}} to add a bookmark to this page, so that you can go back to it quickly.
==== Assigning your report a persistent (DOI-style) identifier.====
Use [http://spectradspace.lib.imperial.ac.uk/url2handle/ this tool] to assign a shorter identifier for your report (one that can be invoked using eg <nowiki>{{DOI|shortidentifier]]</nowiki>.

=== Converters to the Wiki format ===
#Convert a Word document. Open it in '''OpenOffice''' (rather than the Microsoft version) and '''export''' as Mediawiki. Open the resulting .txt file in eg WordPad, select all the text, copy, and then paste this into the Wiki editing page. You will still have to upload the graphical images from the original Word document separately.
#There is also a [http://labs.seapine.com/htmltowiki.cgi HTML to Wiki] converter which you can use to import HTML code from an existing Web page into a (Media)Wiki.

== Basic editing ==
An [[Mod:inorganic_wiki_page_instructions|introductory tutorial]] is available which complements the information here.
*A [http://en.wikipedia.org/wiki/Wikipedia:Cheatsheet cheatsheet] summarises the commands with a [[It:projects|playpen]] for playing. You can write your report by simply typing the appropriate text as shown in the cheatsheet, or by using the WikEd buttons in Word-style composition.
*[[Image:report12345.jpg|right|thumb|The editing environment]]You will need to create a separate report page on this Wiki for each module of the course. Keep its location private (i.e. do not share the URL with others).
*The WikED toolbar along the top of the page has a number of tools for:
**adding citation references,
**superscript and subscripting (the H2O WikEd symbol will automatically do this for a formula),
**creating tables
**adding links (Wiki links are internal, External links do what they say on the tin)
**# local to the wiki, as <nowiki>[[mod:writeup|text of link]]</nowiki>
**# remote, as <nowiki>[http://www.webelements.com/ text of link]</nowiki>
**# Interwiki, as <nowiki>[[w:Mauveine|Mauveine]]</nowiki>
**# DOI links are invoked using the DOI template <nowiki>{{DOI|..the doi string ..}}</nowiki> or the more modern form <nowiki>[[doi:..the dpi string..]]</nowiki>
**# Links to an Acrobat file you have previously uploaded to the Wiki can be invoked using this template: <nowiki>{{Pdf|tables_for_group_theory.pdf|...description of link ...}}</nowiki>
**# There are lots of other [[Special:UncategorizedTemplates|templates]] to make your life easier such as the [[w:Template:Chembox|ChemBox]]
**If you need some help, invoke it from the left hand side of this page.
*Upload all graphics files also with unique names (so that they do not conflict with other people's names). If you are asked to replace an image, '''REFUSE''' since you are likely to be over-writing someone else's image!
** Invoke such an uploaded file as <nowiki>[[image:nameoffile.jpg|right|200px|Caption]] </nowiki>
**We support WikiComons, whereby images from the [http://commons.wikimedia.org/wiki/Main_Page content (of ~10 million files)] from [http://meta.wikimedia.org/wiki/Wikimedia_Commons Wikimedia Commons Library] can be referenced for your own document. If there is a name conflict, then the local version will be used before the Wiki Commons one.
***To find a file, go to [http://commons.wikimedia.org/wiki/Main_Page Commons]
***Find the file you want using the search facility
***Invoke the top menu, '''use this file in a Wiki''', and copy the string it gives you into your Wiki page
*** <nowiki>[[File:Armstrong Edward centric benzene.jpg|thumb|Armstrong Edward centric benzene]]</nowiki>
*Colour can be added (sparingly) using this {{fontcolor1|yellow|black|text fontcolor}} template. (invoked as <nowiki>{{fontcolor1|yellow|black|text fontcolor}}</nowiki> )
*Save and preview constantly (this makes a new version, which you can always revert to). It goes without saying that you should not reference this page from any other page, or indeed tell anyone else its name.
*'''Important:''' Every 1-2 hours, you might also want to make a [[Mod:writeup#Backing_up_your_report|backup of your report]]. This is particularly important when adding Jmol material, since any error in the pasted code can result in XML errors. The current Wiki version does not flag these errors properly, but instead just hangs the page. Whilst you can try to [[Mod:writeup#Fixing_broken__Pages|repair the page]] as described below, it is much safer to also have a backup!
*You should get into the habit of recording results, and appropriate discussion, soon after they are available, in the manner of a laboratory note book.

== More Editing features ==
=== Handling References/citations with a DOI ===
This section shows how literature citations<ref name="jp027596s">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343. {{DOI|10.1021/ja9825332}}</ref> can be added to text<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref> using the '''<nowiki>{{DOI|value}}</nowiki>''' (digital object identifier) template to produce a nice effect. Citations can be easily added from the WikED toolbar.
*The following text is added to the wiki, exactly as shown here: '''<nowiki><ref name="ja9825332">W. T. Klooster , T. F. Koetzle , P. E. M. Siegbahn , T. B. Richardson , and R. H. Crabtree, "Study of the N-H···H-B Dihydrogen Bond Including the Crystal Structure of BH3NH3 by Neutron Diffraction", ''J. Am. Chem. Soc.'', '''1999''', ''121'', 6337–6343.{{DOI|10.1021/ja9825332}}</ref></nowiki>'''
*Giving a reference a unique identifier, such as '''<nowiki><ref name="ja9825332"></nowiki>''' allows you to refer to the same footnote again by using a ref tag with the same name. The text inside the second tag doesn't matter, because the text already exists in the first reference. You can either copy the whole footnote, or you can use a terminated empty ref tag that looks like this: '''<nowiki><ref name="ja9825332" /></nowiki>'''.
*Collected citations will appear below wherever you place the '''<nowiki><references /></nowiki>''' tag, as here. If you forget to include this tag, the references will not appear!
==== Including the DOI for your experiment data ====
The datasets associated with your experiment can be given a DOI by '''publishing''' any entry in the [https://scanweb.cc.imperial.ac.uk/uportal2/ SCAN Portal]. You can include this DOI as a normal citation.<ref name="dataset1"> Henry S. Rzepa, "Gaussian Job Archive for C4H6NO3S(1-)", 2013. {{DOI|10.6084/m9.figshare.679974}}</ref>

==== Additional citation handling ====
* A macro-based reference formatting program has been developed in Microsoft Excel to not only produce the wiki code for direct pasting into your report, but that '''''also''''' formats text for placing in documents, such as synthesis lab reports. This program is available [https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:Reference_Formatting_Program here].
* A '''[[Template:Cite_journal|Cite journal]] template''' is installed for anyone who wants to experiment
----

References and citations
<references />

----

=== Using an iPad ===

[https://itunes.apple.com/gb/app/wiki-edit/id391012741?mt=8 Wiki Edit] for IOS allows a Wiki to be edited using an iPad. You can dictate your text using '''Siri''' if your speed at '''thumb-typing''' is not what it should be.

= Bringing your report to life =
== Basic JSmol ==
You can use coordinate files created as part of your work (in CML or Molfile format) to insert rotating molecules for your page.
#Using your graphical program (ChemBio3D or Gaussview), '''save''' your molecule as an '''MDL File''', which has the extension '''.mol''', or as '''chemical markup language''', which has the extension '''.cml'''.
#Or, if your calculation ran on the SCAN batch system, '''publish''' the calculation, and in the resulting deposited space, download the .cml or the '''logfile.out''' file to be found there (the latter should be used for vibrations only).
#On the Wiki, '''Upload File''' (from the left hand panel) and select the molecule file you have just placed on your hard drive as above.
#On your Wiki page, insert <nowiki><jmolFile text="Explanatory text for link">BCl3-09.log</jmolFile></nowiki> where in this example, BCl3-09.log is the just uploaded file.
##The should produce <jmolFile text="this link">BCl3-09.log</jmolFile>. When clicked, it will open up a separate floating window for your molecule.
##Further actions upon the loaded molecule (such as selecting a vibrational mode and animating the vibration) are done by right-mouse clicking in the Jmol window.

#When using animations, please let them pop up in a separate window using the <jmolAppletButton> function. Your browser won't slow down and you will make your life so much simpler. =)
##Read more on how to do that [http://wiki.jmol.org/index.php/MediaWiki#Jmol_applet_in_a_popup_window here ]. --[[User:Rea12|Rea12]] 20:58, 8 September 2014 (BST)

== Advanced JSmol ==

A much more powerful invocation is as follows. The following allows a molecule to be directly embedded into the report, and it also shows how to put a script in to control the final display.
{| class="wikitable" border="2"
|-
! copy/paste either of the two sections below into your own Wiki
|-
|<pre><jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>yourmolecule.cml</uploadedFileContents>
</jmolApplet>
</jmol>


<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script><uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol></pre>
|-
! First molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])
|-
|<jmol>
<jmolApplet>
<title>Pentahelicene</title><color>white</color><size>300</size>
<script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script>
<uploadedFileContents>pentahelicene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! Second molecule (if you see yellow below, then check the [[Mod:latebreak#Firefox.2C_Java_and_the_Wiki|late breaking news]])

|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;
</script>
<uploadedFileContents>BCl3-09.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Every time you embed a molecule in a Wiki page in the above manner, the Web browser must set aside memory. Too many molecules, and the memory starts to run out, and the browser may slow down significantly. So use the feature sparingly, only including key examples where some structural feature would benefit from the rotational capabilities.
It is [http://chemapps.stolaf.edu/jmol/docs/ possible] to add many other commands to the JSmol container above. For example, '''<nowiki><script>select atomno=3,atomno=4,atomno=5; color purple;measure 3 5;measure 5 4;</script></nowiki>''' will colour atoms 3 4 and 5 (obtained by mouse-overs) purple, and then measure the length of the 3-5 bond. Further examples of how to invoke Jmol are [http://www.mediawiki.org/wiki/Extension:Jmol#Installing_Jmol_Extension found here], and a comprehensive list [http://chemapps.stolaf.edu/jmol/docs/ given here].

== Incorporating orbital/electrostatic potential isosurfaces ==
The procedure is as follows
# Run a Gaussian calculation on the SCAN
# When complete, select ''Formatted checkpoint file'' from the output files and download
# Double click on the file to load into Gaussview
##To generate a molecule orbital, '''Edit/MOs''' and select (= yellow) your required orbitals.
##* '''Visualise''' and '''Update''' to generate them
## To generate an electrostatic potential, '''Results/Surfaces and Contours''', then '''Cube Actions/New Cube/Type=ESP'''. This will take 2-3 minutes to generate
##* In '''Surfaces available''' pre-set the Density to '''0.02''' and then '''Surface Actions/New Surface'''. Try experimenting with the value of Density for the best result. Save the cube as per below.
# In '''Results/Surfaces and contours''' from the '''cubes available''' list, select one and '''Cube actions/save cube'''
# Invoke [http://www.ch.ic.ac.uk/rzepa/cub2jvxl/ this page] and you will be asked to select your cube file,
# followed by three file save dialogs, one for the coordinates (.xyz), one for the MO surface (.jvxl) and a shrink-wrapped bundle (.pngj).
# Insert the following code into your Wiki, replacing the file name with your own choice from the preceding file save dialogs.
<pre><nowiki><jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol></nowiki>
</pre>
# [[image:absolute_path.jpg|right|350px]]Next, upload these two files into the Wiki (one file at a time, the multiple file uploader does not seem to work for this task)
## Now for the tough bit. You will need to find the absolute path for the .jvxl file. Above, this appears as images/1/1b/AHB_mo22-2.cub.jvxl
## Just after uploading a .jvxl file, you will see a response as shown on the right.
## Right click on '''Edit this file using an external application'''. You can used any text editor (Wordpad etc).
## This text file will contain something like: <tt>; or go to the URL <nowiki>https://wiki.ch.ic.ac.uk/wiki/images/1/1b/AHB_mo22-2.cub.jvxl</nowiki></tt>
#Select just the string '''images/1/1b/AHB_mo22-2.cub.jvxl''' and paste it in as shown above:
#You should get something akin to:
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;
</script>
<uploadedFileContents>AHB_mo22.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
* You can superimpose two surfaces. Change the script contents above to append a second surface to the first: <pre><script>isosurface color orange purple "images/4/42/AHB_mo22.jvxl" translucent;isosurface append color red blue "images/1/1b/AHB_mo22-2.cub.jvxl" translucent;</script></pre>
* The four colours used in this line can be changed to whatever you consider appropriate.
=== An alternative way of loading surfaces ===
This method avoids the need to specify paths to files as seen above. Instead uses the '''.pngj''' bundle which contains all necessary information and can be invoked by
<pre><nowiki><jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile></nowiki></pre> which produces <jmolFile text="just a link">CF3_mo30.cub.pngj</jmolFile>.
# It only supports one surface (you cannot superimpose two orbitals)
# You can also load other surfaces, such as <jmolFile text="molecular electrostatic potentials">Checkpoint_60018_esp.cub.pngj‎</jmolFile> generated from a cube of electrostatic potential (ESP) values created using Gaussview as follows:
## Download .fchk file from SCAN
## Open using Gaussview
## '''Results/Surfaces & contours/Cube actions/New Cube/ESP''' and then '''cube actions/save cube''' which is how the above was generated. You may have to play around with the value of the density (~0.02).

=== MOPAC orbitals ===
# Run MOPAC from ChemBio3D, selecting '''Compute Properties/Molecular Surface''' from the '''properties''' pane, and in the '''General pane''' specify a location for the output and deselect '''Kill temporary files''' if not already so.
# Upload the '''.mgf''' file so produced to the Wiki
# Invoke as follows ('''MO 35;''' means the 35th most stable orbital for that molecule).
<pre><nowiki><jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>300</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol></nowiki></pre>
<jmol>
<jmolApplet>
<title>MOPAC Orbital</title><color>white</color><size>200</size>
<script>MO 35;mo fill nomesh translucent;</script>
<uploadedFileContents>test.mgf</uploadedFileContents>
</jmolApplet>
</jmol>

== Enhancing your report with Equations ==
*You may have need to express some [http://meta.wikimedia.org/wiki/Help:Formula equations] on the Wiki. This is currently supported only using a notation derived from '''LaTeX''', and as with the Jmol insertion above, is enabled within a '''<nowiki><math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math></nowiki>''' field inserted using the default editor (the SQRT(n) button), and producing the following effect:
<math>\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}</math>

The requisite syntax can be produced by using
*MathType as an equation editor (used standalone or in Word). It places the required LaTeX onto the clipboard for pasting into the Wiki).
*[http://www.lyx.org/ Lyx] which is a free stand-alone editor.
*A more general solution to this problem is simply to create a graphical image of your equation, and insert that instead as a picture.

== Inserting Tables ==
Instead of inserting screenshots of Excel, tables can be produced using MediaWiki markup (see [http://www.mediawiki.org/wiki/Help:Tables this page]), where you can also find lots of examples of different styles of table. However, this can be quite time consuming when you have a lot of tabulated data and need to copy it from somewhere like Excel into ChemWiki. Instead of typing it by hand, you can save your Excel worksheet as a comma separated file (.csv) and then use this [[http://area23.brightbyte.de/csv2wp.php CSV to MediaWiki markup]] convertor. Note that cells starting with "-", e.g. for negative numbers, need a space inserted between the - and | in the output otherwise MediaWiki interprets it as a new row.

Another web-based utility is available called [http://excel2wiki.net/ Excel2Wiki] which can be used to generate MediaWiki code from an Excel table.

== SVG (for display of IR/NMR/Chiroptical Spectra) ==
[[File:IR.svg|300px|right|SVG]]SVG stands for '''scaleable-vector-graphics'''. Its advantage is well, that it scales properly (but it has many others, including the ability to make simple edit to captions etc using Wordpad or similar). From your point of view, it is readily generated using Gaussview. If you view an '''IR/NMR/UV-vis/IRC/Scan/''' spectrum in this program, it allows you to export the spectrum as SVG (right-mouse-click on the spectrum to pull down the required menu). Upload this file, and invoke it as <nowiki>[[File:IR.svg|200px|right|SVG]]</nowiki> If you open eg IR.svg in Wordpad (or other text editor), you can edit the captions, font sizes etc (its fairly obvious). Oh, you will need to use a web browser that actually displays SVG. Internet Explorer 8 does not (9 is supposed to). Use Firefox/Chrome/Safari etc.

== Chemical Templates ==
An example is the [[w:Template:Chembox|ChemBox]]. Volunteers needed to test/extend these!

= Submitting your report =
For the '''combined synthetic and organic''' experiment submit your Wiki personal URL as obtained above to [mailto:Org-8@imperial.ac.uk?subject=Computational_lab_1C Org-8@ic.ac.uk] with a deadline of the Friday of the second week of any 2-week experiment at '''12noon'''.

For the '''Computational Chemistry Lab''': inorganic and physical submit your wiki URL address on Blackboard by 12:00 on the friday of the 2-week experiment.

= Backing up your report =
[[Image:export1.jpg|left|250px]][[Image:Export2.jpg|right|200px]]Invoke [[Special:Export|this utility]] to back your project up. In the box provided, enter e.g. '''Mod:wzyz1234''' being the password for your report. This will generate a page (right) which can be saved using the Firefox '''File/Save_Page_as''' menu. Specify '''Web Page, XML only''' as the format, and add .xml to the file suffix. You might want to do this eg on a daily basis to secure against corruption. This is in addition to the notes for how to repair broken pages.

The same file can now be reloaded using [[Special:Import|Import]].

= Fixing broken Pages =
There are several ways in which a page can break.

*We have had instances of people inserting a corrupted version of the Jmol lines into their project, resulting in a '''XML error''' or '''Database error'''. Recovering from such an error is not simple. So we do ask that you carefully check what you are pasting into the Wiki, and that its form is exactly as shown above. For example, below is a real example of inducing such an error. Can you see where the fault lies? (Answer: the <nowiki><jmol></nowiki> tag is not matched by <nowiki></jmol></nowiki>. If tags are not balanced, XML errors will occur).
<pre><jmol><jmolApplet><title>equatorial</title><color>white</color>
<size>200</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>Pl506_14_equatorial.mol</uploadedFileContents></pre>
*Another example might be wish to indicate a citation using <nowiki><ref>...details </ref></nowiki> but in fact end up entering <nowiki><ref> ...</nowiki> (i.e. missing out the <nowiki></ref></nowiki>)
*If you do encounter such an error, try invoking your project as '''<nowiki>https://www.ch.ic.ac.uk/wiki/index.php?title=Mod:wzyz1234&action=history</nowiki>''' and edit and then save an uncorrupted version. You will need to be already logged in before you attempt to view the history in this way, since logging in '''after''' you invoke the above will return you not to the history, but to the corrupted page (Hint: it sometimes helps to check '''Remember my login on this computer''' as you log in). For example, the history for this page can be seen [https://www.ch.imperial.ac.uk/wiki/index.php?title=Mod:writeup&action=history here]. You can eg load this preceeding page, and then use it to replace '''writeup''' with your own project address.
*If the preceeding does not work try the instructions shown [[mod:fix|here]].

= Feedback =
Each Wiki page has a discussion section, including your submitted report page. This latter will be populated with comments about your report within a week of submission.

See also: [[Mod:Cheatsheet|cheatsheet]]

Mod:intro

2015-10-07T16:30:07Z

Mjbear:

Mod:intro

2015-10-07T16:25:51Z

Mjbear: /* Report submission */

See also: [[http://wiki.ch.ic.ac.uk/wiki/index.php?title=Main_Page#Third_Year_Computational_Chemistry_Lab|Comp Chem Lab]], [[Mod:latebreak|Breaking news]], [[mod:laptop|Laptop use]], [[Mod:lectures|Intro lecture]], [[mod:programs|Programs]], [[Mod:inorganic|Inorganic]], [[Mod:physical|Physical]], [[Mod:writeup|Writing up]]



== Specific times ==

*Week 2 (Friday): '''submit the wiki address for your report on Blackboard by 12:00'''
**You can submit your wiki address early (before 12:00) and continue to edit your wiki up to 12:00.
**Any material added after 12:00 will not be marked (unless you have been granted an extension)

== Locations ==
Work in the computer lab on Level 2 (232A). 


== Expected hours in the Lab ==

The lab times are 14:00-17:00 on Mon, Tue, Thur and Fri. You not restricted to these times, but you should be able to complete your computational experiment over two weeks and write up in the time available. It is up to you to manage your time: do not do too much or too little. Ask a demonstrator or staff if you are at all unsure.


No student is expected to spend more time on an individual computational experiment than they would on an experiment in any 3rd year lab based course.


Address your questions to the demonstrators during the lab hours they are available. Some will be contactable via email. If you are struggling with the suggested times allocated for each part of the experiment, seek help from a demonstrator.

== Demonstrator and Staff help and feedback times ==
'''Demonstrators are available Mon, Tue, Thur and Fri in the upstairs / Level 2 computer room, usually from 14:00 to 15:00.'''

If you have a question, talk with a demonstrator first. Demonstrators are not just there to help with specific technical questions, they can also offer '''feedback''' on completed work before it is marked.




== Report submission ==

Submit the URL for your Wiki report from [https://bb.imperial.ac.uk/webapps/blackboard/content/listContentEditable.jsp?content_id=_266665_1&course_id=_1962_1&mode=quick&content_id=_308976_1 this address] by the deadline. These deadlines are on the Friday of the end of the second week of each experiment.

You should expect to get a grade on blackboard within 10 working days. If you have heard nothing and have not received a grade in blackboard, please contact the staff responsible for the experiment to make sure your work has not gone missing.

'''Please note the College policy: work submitted late will receive zero marks.''' Any sections completed by the hand-in date will be assessed for full marks, additional material added after this will not be marked. If you are having problems, are ill or have extenuating circumstances please see [mailto:laura.patel@imperial.ac.uk Dr Patel] as early as possible, extensions may be granted and will be determined on a case-by-case basis.

== Lab overview: ==
=== The core modules on offer: ===
Each of the lab modules introduces new types of computational chemistry techniques and their applications. Some of these computational methods involve only a few seconds of actual computing, and are easily accomplished on a laptop computer interactively. Others may run for many hours, and are best done in ''batch'' mode on a computing cluster. You will learn how to handle your laptop computer as "a laboratory instrument", delivering a variety of information about moleculer systems.
=====Module 1: Bonding analyses using ''Ab initio'' and Density functional techniques. =====
=====Module 2: Reaction mechanisms and transition states.=====

The nature of the topic requires a different mode of presentation to the usual word-processed document. You will instead present your results in the form of a '''Wiki page''' unique to yourself. The course documentation also takes the form of a Wiki, and '''''YOU''''' as well as the course organisers can contribute to the instructions. If you feel you can improve on aspects of the documentation, or ''e.g.'' add further key literature references etc (very much in the spirit of the Wikipedia itself), do please go ahead and take the plunge!

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See also:[[http://wiki.ch.ic.ac.uk/wiki/index.php?title=Main_Page#Third_Year_Computational_Chemistry_Lab|Comp Chem Lab]] [[Mod:latebreak|Breaking news]], [[mod:laptop|Laptop use]], [[Mod:lectures|Intro lecture]],[[mod:programs|Programs]], [[mod:organic|Module 1]], [[Mod:inorganic|Inorganic]], [[Mod:physical|Physical]], [[Mod:writeup|Writing up]]