Charge transfer

My new paper just became available online (DOI: 10.1063/1.3526697). The purpose was to present and test an ab-initio approach to simulate charge transfer dynamics. Aside from that we discuss some of the theory behind it and how it applies to direct non-adiabatic simulations, in particular the relation between Landau-Zener theory and Marcus theory. As a model we looked at hole transfer between two ethylene molecules bridged by up to three formaldehyde molecules.


Of course the next step is to extend the approach to more interesting systems. But the nice thing was that most of the physcially important parameters could be adjusted easily. So it was a good way to learn the basic phenomena of charge transfer.

I showed in a previous post what such a dynamics looks like. Here I want to talk a little bit about some of the math behind it. Before we did this work, I never really understood what a non-adiabatic coupling vector was. I will briefly describe that now - for a longer explanation you can of course download and read our paper.

The components of the non-adiabatic coupling vector
are obtained as the derivative of the electronic wave function of one state projected onto the wave function of another state. R_j means the displacement of a nuclear coordinate. Note that this is a derivative in the Hilbert space of electronic wave functions, parametrically dependent on nuclear coordinates.[1]

The interpretation comes when using the mixing angle η between diabatic and adiabatic functions. Because it turns out that
What I am doing now, is to start with a delocalized charge (η=π/4) and localize the charge (η=0) by changing the bond length alternation.

At an intermolecular distance of 5 Angstrom, the interactionbetween the fragments is quite large. The wavefunctions change slowly over a wide geometric range and you have a wide peak of the coupling vector accordingly.

At an intermolecular distance of 7 Angstrom, the interaction is almost vanishing. The wave function localizes after only a small geometric displacement. Accordingly there is a highly peaked coupling vector.

According to the second equation above, the area under both curves is π/4. If you look at the graphs you can see that this could be right, i.e. the area should be about unity.

---

[1] Similar difficulties occur in the derivation of the Hellman-Feynman theorem - in that post there is even the third component λ which represents the possibility of having a not converged wave function...

No slides, no sympathy

Is it rude to walk out of a boring talk or a social responsibility?

Many things can happen with a talk: the accoustics may be bad, the speaker may be nervous. It's even ok if he/she is not so firm with every underlying detail. But for me the borderline comes when the speaker does not even care enough to prepare slides.

I was really excited about a public talk about Schrödinger "50 Years After". I just like the discoveries in those times and the stories behind them. And it seemed to be a possibility to show my girlfriend a little bit of what I am doing. I even cut track practice short to get there on time. But what happens: This man just starts reading in a monotonous voice. People start falling asleep. No slides or anything exciting to wake them up.

It is a petty in my opinion: It would take about five minutes to prepare slides that contain the names of the scientists mentioned. 10 more minutes to get their photos out of google. Maybe an hour to prepare some graphics. Then people could at least take a little bit home. And he does not even do it himself - a lot of people (including me) would be happy to see things they prepared in a big auditorium.

So I just walked out when I noticed that my girlfriend was falling asleep. It is not so much that I minded sitting there for another half an hour. I just think it requires a statement if a speaker does not even care enough to prepare slides.

Atkins

The book I am currently reading is Robert Atkins' "New Diet Revolution". It is not that I am trying to lose weight but I just wondered what is behind it. And I think he has a lot of good points that standard nutritional theory has not fully appreciated yet.

The main claim of Atkins is that sugar and refined carbohydrates are more problematic than fat. This goes for both health and weight issues. I did not realize this initially but it makes sense. To make an analogy: flooding the organism with sugar is like pouring oil into a fire - you are adding highly reactive fuel. In more chemical terms: glucose being an aldehyde is a reactive molecule. And if too much is present it will cause problems, for example react with the amino groups of proteins - the Maillard reaction. What does the body do against it? Produce insulin to make sure all the energy is stored in a safe place - as glycogen or fat. And if everything is stored, there is probably enough excess insulin to lower our blood sugar level enough for the next hunger attack and cravings of carbohydrates. Aside from increasing fat tissue, too much insulin production may eventually also overstrain the pancreas and cause diabetes.

Another interesting point is that food energy, i.e. "Calories", is not everything. The idea is that the standard oxidation energy determined in a bomb calorimeter cannot necessarily be transferred 1:1 to energy available for the body. Atkins states that he has examples where a person would gain weight when consuming a specified amount of calories in carbohydrates and lose weight when they would consume the same amount of calories in fat. The energy conservation law also holds in biology of course, so where does the energy go? Probably into body heat. This leads to what another interesting nutritionist, Udo Pollmer, says: That people on a diet (which is probably low fat) feel cold quicker. [1]

As I just discussed, calorie counting (which seems a natural application of the energy conservation law) may not even make sense from a purely biochemical point of view. A point which is probably more important, that both Atkins and Pollmer mention, is psychology. Basing a diet on severely restricting yourself on such an abstract thing as the number of calories does not work for most people. The body has a built in mechanism to control food balance and it seems difficult to fight that with willpower. Eventually one would just stop the diet and "binge eat". Or maybe your body will get the calories it wants in a more subtle way, for example through high calory drinks (cola, fruit juices, alcoholic beverages, milk, ...). So what restricting calories does, is probably just telling your body that food is scarce and it should try to get as much as possible from wherever it can.

---

[1] edit: actually another reason is that in ketosis energy is lost in chemical form, i.e. high energy molecules like ketone bodies are excreted.

The Double Helix

A very interesting book I just read is James Watson's "The Double Helix", his account of the discovery of the structure of DNA. It is a very fun to read story, showing how they finally came up with the double helix structure and the famous Watson-Crick base pairing. It also gives a lot of examples of how science should or should not be done. It is intersting to see how inefficiencies in the system and personal hostilities had to be overcome before the discovery was possible. He has a very interesting personal and funny writing style but is in some cases a little bit harsh, especially against co-researcher Rosalind Franklin (for which he apologizes in the epilogue, though).

I think the key to Watson's success was interdiscplinarity.[1] Only by bringing together x-ray data, experiments from organic chemists, and his own model building was it possible to solve such a complex structure with the intstruments available in the 1950s. Francis Crick is described as a genius, but as a character who most people could not deal with easily. Rosalind Franklin appears as an excellent cristallographer but threatened by a male dominated world. Sir Lawrence Bragg was the head of the institute who could see how his famous equation lead through this breakthrough discovery.

The race starts with Linus Pauling's discovery of the protein α-helix. After that, Watson and Crick as well as Pauling come up with a triple helix for DNA, with the backbone inside. Franklin has some clear evidence that the backbone should be outside but does not open up her data for display. Eventually Watson tries out models with the bases inside and the backbone outside. It is stimulating to hear of his excitement as he develops the concept of base pairing. For his success he had to collect information from quite a number of people. Franklin and her boss Maurice Wilkins provided the x-ray data. Crick was able to derive and solve the diffraction equations for helices. The work of Erwin Chargaff provided the vital clue that the amounts of adenine and thymine, as well as, cytosine and guanine, were equal. A direct connection to structural chemists was important to get the correct tautomers of the bases (which were wrong in many textbooks at the time). Watson's final discovery was that he could form AT and GC base pairs which had about the same shape - therefore yielding a regular helix. To compare the results to the x-ray data they had to create a molecular model. At that time that meant putting it all together into a large metal model after asking the workshop to make the pieces. Finally everything worked out and they could publish their paper with the nicely understated final sentence:

It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.

A point worth mentioning is the secrecy. It seems that the structure could have been found much quicker, had Wilkins and Franklin released their data earlier. I don't know if this is different in today's "publish or perish" situation, that many results are released as soon as they come. And that they are not kept in secret for so long. But maybe for the big things it is still the same.

Finally it was interesting to read how Watson seemed to be living a very easy going life while he made the most crucial discovery of base pairing. Maybe I should tell that to my boss more often: "When Watson invented base pairing, he played tennis every afternoon. Bye!" At least as far as creative break through work is concerned, flexibility seems to be very important. That is what Lee Smolin points out in his book "The trouble with physics". But I guess a large part of my work is just related to more or less standard data production. That could mean it would be better if I go to work at /:30 and wear a tie...

---

[1] Interdisciplinarity is a little bit overly popularized these days but I think it is still an important feature to be able to look beyond the narrow horizon of one specific field.