Blog ethics

My ankle is still not quite as good as it's supposed to be. Therefore I am still spending more time in front of my computer than I would like to. And with time distribution when studying, no not procrastinating, I got to visit more blogs than usually. Two important questions came to my mind.

The first one: Are blog writers with black blogs better people? I have to disappoint you: no not in general. Someone apparently suggested that at nOnoscience. The idea was that people should use Blackle instead of google. Showing a black screen should take up less energy than a white screen. But this is apparently only true for CRT screens, not for LCDs. So black bloggers: you are only better people if your readers have CRTs, not in general.

I guess a better approach would be just turning your screen brightness down.

The second question is even more important: Should I keep reading R-rated blogs? I found this important tool on a blog that is itself R-rated. It tells you what audiences your blog is appropriate for. The disturbing truth: most of the blogs I read are R-rated. It was no wonder with Ψ*Ψ/Excimer and Kyle. But even Mitch who I thought was responsible couldn't keep himself and his co-bloggers down. Even worse: I need parental guidance to read Albert's posts. And don't tell me words aren't as important as content. I am already disenchanted.

Hemoglobin

I stumbled across hemoglobin while I was studying for toxicology. The body's oxygen carrier is a pretty cool molecule. Here are some pictures that I drew in PyMOL during little "studying breaks". They are made from the XRD structure from Protein Data Bank. Thinking about it, it seems pretty cool that we can actually visualise molecular structures and that we get the same results when we model them in a computer.

On this one you can see the whole tetramer. The four heme groups are shown in yellow.

Heme is the center-piece of the molecule (or as they say prosthetic group). The O₂ is right in the middle. Underneath is the Fe²⁺. It's bonded to the oxygen, the 4 nitrogens of the porphyrin ring, and the nitrogen of His⁸⁷ which is the covalent connection to the protein (hence prosthetic group).

A hydrogen of His⁵⁸ is very close to the O₂. Good for it that it is bent away. You could imagine that linear CO wouldn't be quite as comfortable in there. This is probably one of the reasons why the affinity of hemoglobin for CO is much lower than that of isolated heme.

This is heme with its whole subunit. You can see how the two histidines (the covalently bonded one and the steric hindrance) come from different helices.

Doing all this makes me wonder which I like better quantum chemistry or theoretical biochemistry. I'll get to take a glance into both of them this summer hopefully. Maybe I'll know more then.

jmol troubles

Jmol is such a cool program that not using it in my blog is not an option. The problem is that it causes weird error messages. If you had problems accessing my blog the last couple of days, it's because of jmol. The weird thing is that it works alright if you click a link that leads you here. But if you type the address into the address line, it doesn't work. I know one thing: the problem wasn't with the jmolInitialize command. It doesn't seem to matter to call it several times on a page. The routine jmol.js was programmed in a way that it is just skipped if it's called a second time.

If you weren't able to access my blog, these are the posts that caused the trouble: Methane vibrations, p-Cresole vibrations. Take a look if you haven't been able to. And don't tell me they are not cool.

Cellobiose (2)

I took a second quick look at cellobiose.

I was wondering if you could see the hydrogen bond (in the center) in the MO scheme. So I checked out the orbitals with a large coefficient at that hydrogen and found two with a strongly bonding interaction. MO 41:

MO 54:

The 53^rd MO doesn't fit in (it has even an antibonding interaction) but it looks kind of cool.

Ok, that's it I have to be studying these days. There are a few exams in the coming last two weeks of our semester that I want to take. A last outlook into different fields before it all comes down to theoretical chemistry next year. I finally have to say that thermal engineering is kind of cool with all its balances. As long as you don't actually have to build the machines.

Cellobiose

Cellobiose is interesting because it is the building block of cellulose. As I understand it, the important structural feature is the hydrogen bond between the ring O and the 4' OH. It gives rigidity to cellulose strands.

In my GAMESS 3-21G calculation the hydrogen bond has a bonding order of .08 which is not really a lot. But this may just be a problem of the calculation. I don't know how to add extra functions just to the atoms I am interested in. And even the way I did it, it took 3 hours of geometry optimisation and it wasn't even quite stationary then.

This post is mostly to show a few nice pictures, though. I like making them and it seems that most of the google hits are going for them. Here's another one.

To give credit to all the nice free (or formerly free) programs I used: The structure was drawn, MM optimised and semi-empirically optimised in ArgusLab. Then I rearranged the structure with PyMOL's sculpting function to get the O and OH together. Structure optimisation in GAMESS, data extraction in ChemCraft, pictures again in PyMOL.

Methane vibrations

Lightnir told me how to properly use jmol in blogspot. If you can read this it actually worked. The problem is that if the jmolInitialize command is called in different blog posts, the browser tends to crash. What I did is: I created a new "HTML/Javascript" section with jmolInitialize in it and dragged it up, so it is executed before the post section. - but this doesn't really seem to help.

I am not really a chemoinformatician though. So let's go back to chemistry. Today's molecule is methane. I optimised its geometry and calculated the vibrations in GAMESS. Since the best is just good enough I used a triple zeta basis with a bunch of polarisation and diffuse functions. For methane it is no problem because of the high symmetry. And for the geometry optimisation there is only one variable parameter.

Methane's 9 modes are grouped into 4 different symmetry races (and frequencies). They are T_i (3240/cm), A₁ (3140/cm), E (1670/cm), T_j (1460/cm). I am afraid I don't know if the 3-dimensional races are T₁ or T₂. Again the frequencies are too high, mostly because anharmonicities are neglected. Before you read on you can ask yourself which ones are IR active.



Only the two T races are IR-active. You can tell from looking at them. I guess you could tell from the character table, too. Again I don't know how to. Maybe in a year I so I will know some more. For now it's all about the funny moving molecules.

Another thing to consider: there are 6 IR-active modes in methane (since the two T races are 3 times degenerate). That's why it's such a strong greenhouse gas.

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The IR-active races are apparently T₂ as mevans told me. The idea is that the (x, y, z) functions, which describe light, are of that race. In this case (xy, yz, zx) is also T₂. Therefore Raman spectroscopy would give the same frequencies as IR-spectroscopy.

Dimensionless

In my life there are no pretty pictures or pretty colors but how about some pretty maths?

Chemical engineering, which is my current lab, is much too applied for me but I do like the maths behind it. This is an example of why it is useful to use dimensionless quantities. The prove comes from myself but I don't think it's wrong. For more information you can check out information on the Buckingham π theorem.

We assume that for any stirrer type the power (P) needed to run a stirrer depends only on the diameter (d), the rotational frequency (n), the density (ρ) and the dynamic viscosity (η).

We can divide by P and get rid of the dimensions on both sides.

Since the right side has no dimension one has to be able to rewrite it using dimensionless quantities A_i (or the dimensions wouldn't cancel out).

Because only multiplication and exponentiation changes the unit, we can consider only A_i of the following form without loss of generality [1] (the c_A are rational numbers).

The quantities are made up of three units: kg, m, s. If we want A_i to be without dimension, all three units have to cancel out. This comes down to a homogenous linear equation system.

The solution is a 2-dimensional space.

We just have to pick 2 dimensionless quantities (let's call them Ne and Re) and all the others can be made up as linear combinations (in our case that means multiplication and exponentiation). The equation can be rewritten as (with a 2 variable function H)

We were interested in the power. That means one quantity shouldn't include P. Then only one solution (a 1-dimensional subspace) remains. We choose the smallest whole coefficients and get the Reynolds number.

The other number we choose is the Newton number (there is no strict reason why we took it).

Since we were able to explicitely express P we can also express Ne and we get a function f of one variable.

Now we can start experimenting. We only have to determine the function f for one stirrer size, frequency, medium density and viscosity. Then we can change any of the parameters and know what happens. The problem is that the initial assumption was only a simplification and we have more parameters. That's why it's not quite as nice.

Anyway this is a pretty cool example of how a little bit of abstract basic mathematics can save a lot of work. 1 hour at your desk doing maths can save you 2 weeks experimenting. Or how does that saying go?

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[1] If you want mathematicians to like you, you have to say "without loss of generality" as much as possible.

p-Cresole Vibrations

I destroyed my ankle at a basketball tournament in Berlin. Now I am chained to my desk and lovenox is my only excitement (I don't get why it's ok to call a drug lovenox). So how do you entertain yourself on a friday night when you are not allowed to leave the house? You could calculate the vibrations of p-cresole and find a way to incorporate them into jmol (I could also study for an exam but I don't feel like doing that until the labs are over).

p-Cresole is about the borderline for what you can do ab-initio at your home computer. I drew the structure in Ghemical-GMS and optimised it and calculated the vibrations in GAMESS (US). To get fairly decent results you need much more than a minimal basis for vibrations. I took TZV which is kind of overdoing it maybe. The modes are still 5-10% too high but it did not improve compared to 6-311G. A problem is that the structure wasn't totally optimised even after 20 iterations that took about an hour. And the program tells me that the result is not valid because of that but I think the energy gradient was low enough.



Before you read on you can try to think of the infrared spectrum of the substance.

For 16 atoms there are 42 vibrational modes. I picked a few representative ones. A nice program for looking at them is ChemCraft. But that way I couldn't show them here. So I wrote a Visual Basic script that extracts the information out of the .out file and makes an .XYZ+vib file out of it that jmol can use.

The shown frequencies are proportional to the actual frequencies where 1600/cm corresponds to 1s cycle time.

The highest wavenumber is the OH stretch (4056/cm according to this computation).


Next come the aromatic C-H stretches (this one with 3302/cm).


Aliphatic C-H stretches are a little bit (lower 3138/cm for this one). Normally the borderline should be 3000/cm. So we are a little bit too high here.


Aromatic C-C stretches (1756/cm).


Aromatic C-H out of plane bends (938/cm).


A very low frequency vibration (369/cm).

Schrödinger equation

The Schrödinger equation is be pretty basic stuff but it is pretty cool. This is how it comes from the energy conservation law:

We start out with de Broglie (and the theory of relativity)
and we know that all particles are also waves, a typical wave equation being

Just for the fun of it we make the derivative


and we find out that we can get the momentum through deriving the function. Who would have thought that?

Next we define the momentum operator
and we assume that for every possible wave function the following is true (this and the definition of the position operator are the axioms of quantum mechanics):
With this knowledge we can look at the energy conservation law of mechanics (T ... kinetic energy, V ... potential energy, E ... total energy)
The kinetic energy can be rewritten
We can multiply this equation by Ψ
Finally we replace the momentum by the momentum operator