Water cluster design @ Prof Bettens’ lab

[On the whiteboard: hydrogen bonding, illustration of symmetry operations]

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When we think about what makes chemistry interesting, one of the things is that matters are discrete: as we know, the seemingly continuous objects on the macro level, like a block of iron, a flowing river, are all made of particlular units which we call atoms and molecules on the micro level. The different molecular structures enable different properties of matter, and makes the world as we see it possible.

So even our everyday liquid, water, has its peculiar structures, and it is not as simple as (H2O).As we know, water molecules can form hydrogen bonds with one another: You can imagine a H2O molecule to be a very light, V-shaped magnet. The two lone pairs of electrons on the oxygen atom attact positively charged hydrogen atoms in other water molecules, and repulse their oxygen atoms. These interactions give water molecules a tendency to cuddle up into ‘water clusters’. You can see a piece of ice as a huge water cluster, in which all molecules are hydrogen bonded to saturation except those on the surfaces. In liquid water however, there are also tiny water clusters, or, we may call them tiny ice pieces.

Martin Chaplin has proposed, for example, an icosahedral (H2O)280 cluster. It may really exist in liquid water and be used to explain precisely some of water’s properties, like density, heat capacity, refraction index.

What I would like to do is to design more water molecules in order to test Prof Bettens’ method of fragmentation that computes a chemical system’s electrical energy. But we can’t just randomly design. For me, I have followed these steps. Considering the structural properties of water clusters, investigating the technical matters like FORTRAN language and Gaussian, writing a programme to help me generate the structure, using the programme, and lastly, being creative. 🙂

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For the structural considerations, we first note that the oxygen in water is sp3 hybridised, which means it tends to form tetrahedral bonding. This makes the oxygen looks pretty like carbons in alkanes. They prefer five- and six- membered rings. Secondly, we have reasons to believe that a water cluster is rather symmetrical, considering that its enrironment: liquid water, is homogeneous on the large scale after all, which means there is not a direction that is special for liquid water. But I am also not sure why they must be symmetrical. But after all, symmetrical patterns are easier to make, because it is basically the repetition of the same thing. We can simply generate a little piece and do symmetry operations to expand it. These operations include reflection, inversion, ratation, translation, and so on. Mathematically, these can be done by multiplying certain matrices to a coordinate. Let’s see an example.

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Suppose we want to inverse the point (x,y,z) with respect to the centre of inversion (a,b,c), what we do is multiplying the purple matrix to the vector (x,y,z,1). The result is (2a-x,2b-y,2c-z,1), in which the first three numbers are the coordinates of the inversed point. Do this to each atom of a molecule and we can inverse the whole molecule. Reflection, rotation, and so on, all have their specific matrix representations.

The last structral consideration is the socalled Ice Rule. It says the specific orientation of a particular water molecule needs not be unique. For example, (on the whiteboard,) both the structures are plausible. However, overall we must make sure of two things. Firstly, because we are dealing with H2Os, each oxygen must covalently bonded to 2 hydrogens. Secondly, because water molecules are connected by hydrogen bonding, between any two linked oxygens there must be a hydrogen. This hydrogen is covalently bonded to one of the oxygens, therefore closer to it, and ‘loosely’ bonded to another oxygen, therefore further from it. In the case of ice under unusual pressures there are exceptions to the ice rule, but for water clusters it is sufficient to just consider this rule.

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Next let’s see the softwares that makes this task possible. The most important thing is called a Gaussian input file, gjf for short. By doubleclick on such a file we open a text file. By right click and Open, or Open With GaussView we see the corresponding visualisation. The Gaussian input file comprises of 3 parts. The first five lines are file specifications used for calculation of energy, and is not crucial for the current cluster design. The second part is the atoms specifications. The first two numbers are charge and spin of the whole system, followed by the elements and x y z coordinates of all the atoms. The last part is a connectivity table. It takes some time to understand it. For example, the first line ‘1 3 1.0 5 1.0’ means, atom #1 is connected with atom #3 with a single bond, and connected to atom #5 with a single bond.

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Now let’s start programming. My overall algorithm is like this. I get my inspirations from alkanes, in which all carbons are sp3 hybridised. Because oxygens is the skeleton of a cluster, and hydrogens are just used for bonding, I will settle down all the oxygen first, and add hydrogens at last to fulfill the Ice Rule. So to begin with, we draw a simple structure made solely of oxygen atoms using GaussView, save it as a gjf, and ask my programme to read it, do symmetry operations to it, and save the outcome to another gjf. After all the oxygens are in place, I will add hydrogens at the midpoint of each O-O connection, and add more hydrogens connecting to random oxygens so that there are twice as many hydrogens as oxygens. Lastly, I used a tedious algorithm to place all the midpoint hydrogens to ensure each oxygen covalently bonds to two and only two hydrogens.

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I will skip the next two slides as they are about coding. You can just refer to them when you happen to read my code. Just one thing to note: in order to do symmetry operations to not only the atoms but the bonds as well, I mark the midpoint of each bond indicated in the connectivity table, and treat these midpoints as if they were atoms. That is, I multiply the symmetry operation matrices to the coordinates of those midpoints as well, and use the resulting, operated midpoints to genereate a new connectivity table.:) This is not a good way to do symmetry operations to the bonds, but I can’t think of a better way.

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Now it’s time to use this programme. I will use the example of how to build a (H2O)100 cluster. What I start with is this structure with only six oxygen atoms. It is obviously inspired by boat-form cyclohexane. We can draw it on GaussView and save it as input.gjf. Drag the file to the remote computer’s folder, and after this is done, run the programme called mybigexe, and enter ok.

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Next we consider what symmetry operation we can do to it. We can of course do anything, but not all symmetry operations lead to plausible, beautiful clusters. It is a guesswork really. What I did is to reflect the molecule with respect to the plane defined by atoms number 2, 4, and 5. So enter 2 in the control screen…The programme will ask you to define the plane of reflection, so we just enter ‘2 4 5’. Alternatively, you will have to enter ‘0 0 0’ first and enter the coordinates of 3 points of that plane manually to define the plane.

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Now we can open our output.gjf to check the result. Here it is, note that the original atoms are also preserved.

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The programme asks you whether you want to do another symmetry operation. If you want to do another symmetry operation to your original input, enter Y. If you want to save your output as the new input and do symmetry operation to it, enter Z. Here I enter Z and ask the programme to reflect the molecule with respect to atoms number 1 3 6.

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We check output.gjf again and find that we have gotten something like a star. In order to complete it, we add two bonds on GaussView and save it. Then we enter Z again in the control screen, so that this star is saved as the new input. We ask the programme to do rotate the star by 120 degrees with respect to the axis defined by atoms 2 and 5, and get the molecule on the bottom-right. We enter Y and ask the programme to rotate the star by 240 degrees with respect to the same axis. What we get now is a molecule with three-fold rotational symmetry.

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We can do symmetry operations as many times as we like, until it is too complex… Then we simple enter A instead of Y or Z. The programme will take care of all the hydraogens now and open your output.gjf again, you will find your water cluster there! It should work most of the time if your oxygen skeleton doesn’t have hypervalence oxygens. But I believe sometimes this step can go crazy because my algorithm is not mathematically proved to work all the time. Anyway, if you find any problems, please contact me. 🙂 The cluster I make here is already found in nature by these three German chemists,Mueller, Boegger, and Diemann. But I only knew this after I ‘designed’ it. 🙁 Schade! Which I were born earlier…

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But there are other clusters that I have made! Their energies are calculated by Gaussian. The programme is not hard to use, and when one gets used to it, all that needed is creativity. The algorithm of placing the hydrogens is in another article on my blog. Check it out if you are interested.

That’s it! Have fun!!!

 

 

 

 

 

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