Molecular graphics tutorial

So far you have drawn your structure and optimised it. The next step is making a nice looking graphic out of it.

The program that I like to use for this is PyMOL. It works great but I have to admit that I haven't tried any other comparable programs. First you open the molecule file that you just produced. On the right side its name appears. Go there and click zoom. Change the the preset to "ball and stick". Change the color to how you want your carbons and then go for color by element. The carbons will stay the way you had them.

I usually like a 1440x900 picture because that fits my screen. With typing "viewport 960,600" the window is on scale and I can still see everything. I rotate and zoom the molecule until it looks nice. Then I type "ray 1440,900" to raytrace the picture. If I like it I save it. If I don't I can change some of the settings.

PyMOL related links are: the official manual - it definitely makes sense to work through that once. PyMOL scripts - I use a modified pymolrc file to set the background color and the viewport. PyMOLWiki - I haven't really found much information I could use there.

POV-Ray is a raytracing program that can be used in connection with ArgusLab. ArgusLab has an option for exporting into the POV-Ray format. I don't think it is as convenient to use as PyMOL. I don't like the pictures as much either. It probably has much more options but PyMOL has a few very nice looking presets.

jmol offers a possibility for having interactive molecule models on web pages based on java. To use jmol you need a webspace where you put the files for running jmol and the molecule files. The applet appears if you add a few lines of javascript code to your webpage. For using jmol in blogspot I open the .js file in the header. Inside my post I have the following code (there are no line breaks because blogspot will add <br /> and create large spaces):

<div style="border: 1px solid grey;"><script type="text/javascript">jmolInitialize(" .../blog/jmol");jmolApplet(500, "load .../blog/molfiles/BINAP-PM3.mol;");</script></div>

The problem is that the browser crashes if two applets are opened like this on same page. Maybe the problem is that "jmolInitialize" is carried out twice. I might be able to solve the problem if I put that into the header, too. But I am not sure about that and who needs so many moving things anyway. I can't put an applet here for that reason but you can look at BINAP.

Molecular modelling tutorial

I was asked to write something about producing the graphics I am putting on this blog. This post will be about the molecular modelling part. The next one about the graphics.

First you have to pick a nice molecule that caught your interest. I'll stick with ligands. N,N'-Diadamantyl-imidazol-2-ylidene looks kind of cool and I am wondering if modeling carbenes works well. To start out you can do the same things that I am doing with any smaller molecule.

For drawing the basic structure, a typical chemical structure drawing program works best. I like ChemSketch. Other people like ISIS/draw. In there you draw the structure. In my case it looks something like this (the c-hexane rings are 3D-rotated):
As a next step you should add the hydrogens in ChemSketch (this works better than adding them in ArgusLab). For quick qualitative results ChemSketch has an optimisation function.

For molecular modelling with more options you can use ArgusLab. To do that you have to export the structure as a molecule file (.mol, .pdb, or .xyz) and open this file in ArgusLab.

Next you should go for "clean hybridisation" (Ctrl+B). The ring becomes aromatic. After that you set up a geometry optimisation (benzene ring button). For a first optimisation molecular mechanics work best. UFF (universal force field) works, AMBER doesn't for some reason. This is the molecule after UFF.

As a next step ArgusLab offers semiempirical QM for structure optimisation. AM1 (Austin model 1) and PM3 (parametrised method 3) are supposed to be the best ones. In this case I used AM1. If you use a molecule this size optimisation takes quite a while. But that is ok because ArgusLab perfectly works in the background.

At first glance the optimisation doesn't make much of a difference. In the following two pictures it can be seen that bondlengths did change a little bit. An interesting fact is that the second structure which was optimised with QM works better with the resonance structures. The bond in the imidazole that is a single bond in every resonance structure really is longer than the other ones.


TINKER is another molecular modelling package that is based on force fields. But I haven't really figured out what to do with it.

If you want quantitative results, you have to go for ab initio quantum mechanics. For that there is no Shareware program and you need much more computing power. The typical program for this is Gaussian. It is definitely a great program but it has a bad reputation for treating competition in a non-academic way (by academic I mean putting science before profit). If you ever feel like modeling a solid body there is my school's WIEN2k. WIEN2k wouldn't ever prohibit anyone from purchasing a license. They even distribute their source code and everyone using WIEN2k can work on improving it. That's what I mean by academic.

---

Apparently GAMESS is an ab initio program that you can obtain for free. I had been at their homepage before but I was kind of scared then because they only talked about UNIX and self-compiling. But there are also precompiled windows versions for boring half-assed-computers people like myself. I just asked for my registration, I am pretty excited.

BINAP

BINAP got me excited when I read about it at carbon-based curiosities. It's a molecule worth some calculation time in ArgusLab.

The structure was optimised with semiempirical PM3. I guess this should work fine here. You have to remember though that it is a gas phase calculation which may give strange results in some cases. But I guess it's ok here. In my defense I can say that crystalising a substance for x-ray diffraction may lead to unexpected results as well. Or is benzene not a regular hexagon (Proc. Roy. Soc. A270 (1964) 98-110)?

Anyway this is the structure. jmol is too cool. So I used it again. I am sorry if it takes a long time to load. But it should not make your browser crash if I put only one applet there.

The first thing you notice is that the two naphthalenes are in planes almost perpendicular to each other. It makes sense that they will move out of each other's way. Also the π-bond between the rings would be pretty weak even if the system were planar. You can see that from resonance structures. Or you do it the cool way and calculate the Hückel π-bond order. It is only .40 when every other bond has between .5 and .7.

This enantiomere is apparently called R. You look at the two naphthalene rings: if you want to walk upward you have a right turn. A helix scientist might call it left-handed. If he walks down, he has to turn left. You can also think of it as a lefty tighty, righty loosy screw.

The weird thing is: If you look at the molecule from a different perspective then the turn is the other way. But maybe this doesn't count because you can't walk through without jumping down in between.

Metallography

It may be kind of poor that it took me 2 and a half years in chemistry to find out what the difference between cast iron and steel is. Iron just never excited me. But if you leave aside the blast furnace [1], it can be pretty cool. And everything becomes more fun if you have a phase diagram.

This is the inorganic technology lab again, metallography exercise. We did our best to produce some nice pictures without wasting too much SiC and diamond [2]. This post is mainly to show those pictures. I am not going to cover the whole chemistry. But remember we are not van der Voort [3].

Here's (globular grey) cast iron


and here's a steel (at a higher magnification, etched with FeCl₃).

The difference is mainly that cast iron has more carbon in it (more than 2.1 %). When it cools down, graphit forms (unless you cool it down really fast and you get white cast iron). In steel there is ferrite (iron with a little bit of C dissolved) and metastable cementite Fe₃C. Those are probably the two phases above but it's hard to really see something.

We etched the cast iron with nital solution (nitric acid in alcohol). You can see that there are three areas: carbon spheres, carbon depraved ferrite around them and a third one which is a mixture of ferrite and and cementite called ledeburite or perlite.

Perlite is formed at the eutectoid where solid austenite decays. Ledeburite is formed when the eutectic liquid freezes. In both cases ferrite and cementite form and stay in close contact. With 500 fold magnification you can see the two phases.
This is a copper alloy (4% tin, 4% zink, 4% lead). We etched it with FeCl₃.


You can see typical twin crystallites in there.The grey spots are lead that is not miscible with copper in the solid phase.

---

[1] I don't think it is possible for me ever to remember every part of a blast furnace.

[2] Actually "diamond" sounds better than it is. One carat of it which goes for something like 15,000 Euros if used for jewelry, costs less than a Euro if you produce it industrially.

[3] Van der Voort is the man when it comes to metallography. He has never taken a foto with a scratch.

Burnside's lemma (2)

Let's go on with Burnside's lemma. I want to show an example today. The question is how many different dichlorobenzenes there are. Of course for this question you don't need Burnside's lemma but I have to start somewhere.

If we don't take reflexions (because of chirality) then we have to consider the D₆ point group. Let's call it G. X is the set of the 15 fixed dichlorobenzene structures seen in the last post.

What we are doing now is look at all the operations g in G and see how many structures in X stay the same when g is applied. Then you have to average that. The average happens to be the number of isomeric structures.

If you apply the identity E, everything stays the same and you have 15 structures fixed by the identity. There is no structure that stays the same when a 60° rotation (C₂) or a 120° rotation (C₃) are applied. With a 180° rotation around the main axes the 3 para-structures stay the same. For the two sets of 3 rotations perpendicular to the main axes (C'₂ and C''₂), 3 structures each stay the same.

This table summarises this.

n	g	|Xg|	n |Xg|
1	E	15	15
2	C6	0	0
2	C3	0	0
1	C2	3	3
3	C'2	3	9
3	C''2	3	9
12			36

In the last line there is |G| to the left and the sum of the |X^g| to the right. Divide these two according to the formula I showed last time and you get 3 which is the true result: 0, m, p.

I hope I could kind of explain what's going on. It just seems to me that Burnside's lemma is some nice mathematics beyond the typical calculations.