Merry Christmas

Merry Christmas everyone! I hope you had a nice celebration (no matter if it was the 24th, 25th or will be the 6th).

There will be a few more dry days on my blog. I'll be gone to Austria's snowless mountains. Snowless thanks to the greenhouse effect [1]. That means no snowboarding for Christmas break [2].

What's coming up next? I am thinking of talking about one or two more molecules. Visualise their structure in PyMOL or POVRay and talk a little bit about them. Then I want to cover some MO-theory. Some more pictures are coming. I will talk about theoretical aspects and proofs, too. Maybe someone's interested. It also helps me to get my thoughts straight if I write about it.

I guess I will see how people are going to like my blog. If I keep getting a few hits per day I'll probably keep writing. Thanks for recently adding my link to a very decent chemist with a cool blog and thanks to some ingenious muppets who aside from adding my link will soon resolve all my problems about fitting together ground-glass joints of different sizes.

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[1] It might be just statistical deviation that we had almost no snow so far. But in a materialistic world I needed a catchy phrase to get your attention [3].

[2] I am sorry for everyone who may have been caught in a snow storm in the US or London or anyone else who has had bad weather conditions. That is of course much worse.

[3] In spite of the fact that Austria's snowless mountains may not be caused by the greenhouse effect, I am still worried by it. Here is my suggestion to anyone reading this: Try taking your bike to work for once. Not only is it good for the environment and cheaper but it is also nice for athletic reasons [4].

[4] To be honest: I stole the idea of making footnotes of footnotes from carbon-based curiosities. But the idea of making footnotes of footnotes of footnotes I just came up with myself.

Atropa belladonna

I just noticed how fun it is to draw structures of alkaloids. Here comes another one.

The substance is extracted from atropa belladonna. The name is ambiguous as the substance is. Atropos is one of the three Fates and Greek mythology, determining the way a person is going to die. Belladonna is Latin for beautiful woman. Just like Botox it is a neurotoxin (formerly) used in cosmetics.

Atropine works by blocking acetylcholine-receptors. Therefore it inhibits nerve activity mainly in the parasympathetic nervous system. This makes it a neurotoxin, hence atropa. Applied to the eyes it makes the pupils dilate. Since that apparently looks good the plant has the name belladonna. Of course this is really bad for your retina. It is only used for eye examinations any more.



Atropine is actually the name for the racemic mixture between (S)- and (R)-hyoscyamine. The deadly nightshade only contains the S form. It racemices quickly after isolation.



This is (S)-hyoscyamine. At the bottom you see tropa-acid (3-Hydroxy-2-phenyl-propanoic acid). The chiral center is at its second carbon atom. At the top is the bicyclic tropine group.

You do notice a similarity to acetylcholine. Especially if you think of the nitrogen of tropine protonated.



The tropine group is a [3,2,1]Bicyclooctane derivative. [3,2,1] means you have three, two, and one atoms in between the bridges. The cyclohexane ring can be arranged in a chair conformation. You also see a 5-membered and a 7-membered ring. The oxygen is in endo position, meaning it points toward the bigger part of the remaining ring.

Glowing gin tonic (quinine)

I know quinine mostly because of the fact that it makes gin tonic glow. But it has some other nice properties, too. Most important is its use to treat malaria. It also works with other medical conditions. I am just going to talk about its structure, though.



This is its structure as seen on Wikipedia. You notice the Methoxy-quinoline, the bicyclic system called quinuclidine, and methanol in between. There are a bunch of asymmetry centers. The most important one is at the methanol. If you change its configuration, you get quinidine.

Before you scroll down, you can exercise your 3-dimensional thinking. What does the bicyclic system look like? I have to admit that I did not get it. But I don't think it is so difficult.

This is the structure as PyMOL's Ray function makes it. The structure was first drawn in ChemSketch and the geometry optimised in ArgusLab.



We needed the 3-dimensional structure mostly for the quinuclidine. Now it can be seen that it is nothing but 3 cyclohexane rings in boat conformation.



The next question would be if the rings are really this ecliptical. I don't know. It does not seem like you can make a chair in there but you could twist the rings. They were twisted after molecular modelling. But with quantum mechanics they became ecliptical. I would think that QM is more accurate than MM. But I have to admit that I could not really do a good calculation on my laptop since the molecule is fairly big.

Conclusions from functional analysis

Actually I would like to talk about how I got up at 1:30 pm at a day when it already starts becoming dark at 3:30. And how it is to celebrate finishing a lab before I am quite done with all the lab reports. But this would not fit to what my blog's name promises.

What I am talking about today is not really chemistry either but related to it. Maybe it is not interesting to non-mathematicians but I have to post it because I like the conclusion.

I found this book "Lectures in Functional Analysis and Operator Theory"[1] at my grandpa's house. Since functional analysis seems to be a really big thing in theoretical chemistry I took a look into it. What I found out is that a functional analyst is not "sqeamish about using Zorn's lemma", that he "definitely relishes the use of topology", and that "he doesn't stand in the way of the internal algebraic impulses of the subject".

I liked this even though I don't know what topology is and I don't have any idea about the algebraic impulses. But I do know what Zorn's lemma is. We talked about it (squeamishly) in a linear algebra course I took.

Zorn's lemma is equivalent to the axiom of choice. It is used to deal with infinite sets. One interesting conclusion is that it can be used to prove that it is possible to take a solid ball in three dimensional space, cut it up into finitely many pieces, and rearrange the pieces to get two solid balls of the same size (Banach-Tarski paradox).

Does this pertain to a chemist? Do we need such abstract laws with strange conclusions? Well we do. Zorn's lemma is needed to proof that even an infinite vector space has a basis. You need this combined with the spectral theorem to proof the variation principle. And that is something most chemists probably have heard about. It is the basis for pretty much every orbital approximation.

In other words: Next time you look at an orbital, think of the fact that it was derived using the same mathematical principle that states that you can cut up a solid ball into pieces, rearrange the pieces and make two solid balls of the same size out of it.

By the way, I haven't really gotten farther in the book than the text I've quoted. Maybe eventually I will do some extra math and then I will be able to perform some nice Kohn-Sham equations.

[1] Berberian, SK. Lectures in Functional Analysis and Operator Theory. 1974. Springer.

Hybridisation

Today I want to talk about hybrid orbitals. I always used to wonder how they were made and why their name was derived from the greek word for mixing. Now I know that they are nothing but mathematical linear combinations of the original orbitals. I am not going to talk much about theory though because I think that most people who are interested in it already looked it up somewhere. What I want to show now, is a little visualisation of the orbitals. It is supposed to show how a hybrid orbital is made of the 2s and 2p orbitals.

First I was going to make a moving gif. But then I remembered that I hate moving gifs and everything else, moving on my sreen without me asking it to. Actually I don't think I could enjoy the internet without AdBlock. It lets me block out the ads that catch my attention by being most annoying.

So I decided to make this in JavaScript. I found out that Blogspot doesn't support JavaScript. Because of that you have to click on the image first before you can change it.

By clicking the left single arrow you can increase the s-character of the orbital, by clicking the double arrow it is increased automatically. The right arrows work the other way, you go toward the p-orbital.



I hope you can enjoy this as much as I enjoyed making it. You can see how the electron density is transferred to one side giving the possibility for a big overlap with an orbital from a different atom.

The pictures were drawn in Mathematica which is a really nice but also expensive program.

Science sometimes does work

When it comes to labs, I don't think I am much of a synthetic chemist. In fact I don't believe it is possible to get more than 50% "theoretical yield" or that someone is actually performing syntheses with more than two steps. However, now is my physical chemistry lab and it is much easier to make me happy there.

What we did is, suck out all the air out of a flask filled with our analyte substance. After closing the valve we measure the pressure in there which is the vapour pressure. Do that at different temperatures and you can see what the phase boundary looks like. First thing that amazed me is that we actually got a nice looking graph.



So what do we do with this? We just need the laws of thermodynamics and the ideal gas law. We rearrange them a little bit according to Mr. Clausius and Mr. Clapeyron and get their equation (I am not showing the proof even though it is kind of cool):



By using the chain rule we can also say:



The T² cancels out and we get:



That means that we get the enthalpy of vaporisation just from the change of vapour pressure with temperature. Who would have thought that? Let's plot the logarithm of the pressure against the reciprocal value of the temperature:



Make a regression, derive, get the enthalpy of vaporisation:



Why is it getting lower? Even that can be explained. At the critical point there is no difference between the phases. Hence there is no enthalpy of vaporisation. You can expect the enthalpy to become smaller when you raise the temperature because you are getting closer to the critical point.

We can even do more. Extrapolate the curve to standard pressure and get the boiling point at 39°C. Now Mr. Trouton tells us that at standard pressure the entropy of vaporisation for every liquid is about 88 J / (mol K). (It seems that this is thermodynamically derived.)

Can we get the entropy just from this curve? Yes we can. We know that Δ_vG = Δ_vH - TΔ_vS. Since we are at equilibrium Δ_vG = 0. Then Δ_vS = Δ_vH / T (we actually used this equation already the other way around for deriving the Clausius-Clapeyron equation).

Divide the enthalpy at the boiling point by the temperature and you get 75,8 J / (mol K). That is almost what Mr. Trouton said.

It took me some time to appreciate thermodynamics. But now I think it is amazing how all those values are related and how much you can do with it. Actually synthetic chemistry is cool, too (on paper at least).

SPPS

If biological synthesis of proteins and cell-free DNA expression are not flexible enough for you or you consider them inhumane then you have to resort to stepwise chemical peptide synthesis. Since proteins and peptides are an important area of modern research, many efforts have been made to make them accessible by synthesis. In current methods the peptide chain is bound to a solid resin. This makes purification easier. Excess reagents can be washed away without losing product. Even with modern techniques of solid phase peptide synthesis combined with chemical ligation it is difficult to get far beyond 100 amino acid residues.

Last summer I had an internship about protein synthesis. By it I was inspired to play around a little bit with PyMOL, a nice graphics program. If you use it, check out the sculpting function.


The image shows a peptide chain bound to a solid resin (green). The main chain is shown in red, side chains in orange. Side chain functional groups are protected by light blue protecting groups. The amino acid Lysine is in place for the next coupling step. Its α-amino group is protected by t-Boc. The carbonyl is activated by an active ester to Hydroxyazobenzotriazole (purple). The picture is drawn according to literature [1].

A different perspective:


This is what the protein looks like with just sticks.

[1] Miranda, L. P. et al. 2001. Total chemical synthesis and chemotactic activity of human S100A12. FEBS Letters 488 85-90

Adrenaline

For my first post I want to show a few pictures created with ArgusLab. The molecule I am dealing with is adrenaline or epinephrine, a hormone and neurotransmitter. Adrenaline is derived from the amino acid tyrosine through hydroxylation, decarboxylation, and methylation. Adrenaline without the methyl group is called Noradrenaline (notice: "Nor-" means "without methyl" in biochemistry). Another name for adrenaline and noradrenaline is "catecholamines".


Adrenaline is synthesised at the kidneys in the adrenal cortex. It is the bodies short term stress response. It works as a hormone causing typical fight-and-flight reactions like increasing the heart rate and dilating arterioles in leg muscles. It also works as a neurotransmitter in the sympathetic nervous system.

The images of adrenaline I want to show are of the electrostatic potential mapped on the electron density. The shape is determined by the electron density which corresponds to the probability of finding an electron at a specific place. The surface connects all points with a given density.


The color is determined by the electrostatic potential. Negative areas localised at the oxygen and nitrogen atoms are shown in read. Positive hydrogens are white.


Another image of the ESP mapped on the density. This time the drawn density was set to a larger value. So the shape is closer to the molecule.


You can produce different kinds of surfaces. This time only dots are drawn.

Starting a blog

I know starting a blog isn't really a new idea. But I still hope I can contribute with another easy reading blog with a few nice pictures and intersting trivia.

I would like to post pictures of some cool molecules. There are nice free programs like ArgusLab and PyMOL that I can suggest to everyone who's interested in modeling and visualisation. I like producing graphics with them once in a while. These will be shown here.

And there are a lot of amazing things related to chemistry I would like to talk about. Mostly theoretical chemistry, hopefully I can still make them readable for everyone.