UV Excited Single- and Double-Stranded DNA

There is a new paper out by us: "Electronic Excitation Processes in Single-Strand and Double-Strand DNA: A Computational Approach" in Topics in Current Chemistry. I made this figure to show all the possible processes happening:

• Monomer-like decay, which is also observed in the gas phase
• Delocalization and excitation energy transfer (with a focus on electron dynamics)
• Proton transfer between the strands, possibly leading to deactivation
• Electron transfer leading to charge transfer states
• Excimers, which may constitute stable trapping sites
• And finally the thing we are trying to avoid: photoproduct formation, which can lead to damage of the DNA

Which ones of these pathways are the important ones is not known yet. The problem is that every research group involved has their own convictions and it is not quite clear who is correct. In this paper we are of course not able to solve the problem, but at least we discuss the different computational methods applied to help make it more clear why the results by different groups are different.

My own contribution to the debate is the hypothesis of an exciplex with strong geometric distortions, small intermolecular separations, and strong orbital interactions that we described in this paper. Some other groups have obtained similar results: In particular Spiridoula Matsika did lots of work (e.g. this paper) where she invokes a bonded exciplex model. And a Chinese group who were the first to obtain these types of results, using semi-empirical calculations.

The calorie counting paradox

Gary Taubes has an interesting purely mathematical argument against calorie counting in his book "Why We Get Fat". I would put the idea as follows:

Assumption: Our weight is primarily affected by our conscious decisions of how much we eat and excercise.
Consequence: The weight of all of us (except for the most rigorous calorie counters) would fluctuate strongly (several kg per year).

The "proof" goes as follows: If our calorie balance was off by only 20-25 kcal a day, this would amount to about 9000 kcal per year, which corresponds to one kg of pure fat. 20-25 kcal is about one percent of our daily intake. It corresponds to about half a slice of bread or 300 m of jogging, respectively. This is way below the precision any of us can excercise on a day-to-day basis. In other words: if it really were up to our concious minds to maintain energy balance, we'd be in a mess. But this is a contradiction to what we actually observe: there are many people whose weight is stable over a long period of time. So, apparently, on a subconscious level there are strong feedback cycles at work, which overrule our conscious actions.

Of course, nothing is definite in medical science, but I think this is kind of an elegant way to think about such a controversial topic. Thanks to the power of maths, we do not have to rely on indirect information from epidemiological or laboraty studies.

Anyway, if we accept that it is hopeless to try adjusting our weight by quantity of food and excercise, can we do anything? Well, we can go for quality! It is well known that hormones such as insuline, human growth hormone, sex hormones, stress hormones etc. strongly affect our body composition. And we also know that we can affect the production of these hormones by our life style and the type of food we eat. Of course, at this point we do have to go into the (secondary) scientific literature to find out what we should do. But at least we know what questions to ask.

Finally, we should mention that the first law of thermodynamics certainly holds (see also this post), i.e.

calories in = calories out + calories stored

But these are things we cannot affect directly. For "calories in" you need perfect willpower. For "calories out" you need complete control over all metabolic pathways including calories leaving you in the form of heat, not completely metabolized molecules etc. And you have to be extremely precise at that ...

One last thought: the concept of calories is actually quite amazing. You can burn food in a calorimeter and measure by how much water is heated up. The number you get, quantifies the ability of this food to support life. This is a fascinating idea showing the power of abstract physical laws. But it is not the whole story.

Oscillator strengths

What is the physical significance of the oscillator strength? Following Werner Kuhn's arguments (e.g. in this paper), it marks the number of electrons oscillating per spatial dimension during an electronic transition. The sum over the oscillator strengths of all the excited states amounts to the number electrons, which is the essence of the Thomas-Reiche-Kuhn sum rule. In other words, the oscillator strength counts how much of the total oscillating potential is used for a specific transition.

This interpretation explains for example the linear relationship of the oscillator strength of the lowest excited state with system size in the case of some conjugated organic polymers (see e.g. this paper): If there are more electrons available to oscillate, then the transition strength increases.

The oscillator strength f_ij between two non-degenerate states i and j is defined (in atomic units) as two thirds of the squared transition dipole moment multiplied by the energy gap

where the vector r contains all 3N spatial coordinates of the N electrons

The Thomas-Reiche-Kuhn sum rule now states that the sum over the oscillator strengths from one state i to all possible other states is equal to the number of electrons in the system, i.e.

In particular, if we consider excitations from the ground state, then all oscillator strengths are positive. Which means that the oscillator strengths can in fact be viewed as a partitioning of the number of electrons.

The derivation of this sum rule starts by realizing that the momentum operator with respect to any spatial coordinate x of any particle (e.g. x=y₂) is given as the commutator of the Hamiltonian with this coordinate

This follows whenever H is of the form

where clearly the derivatives with respect to x are the only part, which does not commute with x itself

By applying the product rule twice, the first term of this expression becomes

And in summary

The remaining proof follows what is shown here (sorry that I am switching the notation, but I copy-and-pasted a little bit ...). First one realizes that the commutator of x and p_x is equal to i

Then one expands the commutators and inserts a resolution of the identity over the eigenstates of the Hamiltonian

Insert the above expression for p_x

The commutators are evaluated by letting H act either on the bra or the ket, which results in a multiplication with the respective eigenvalue. And after summing together the equivalent terms one obtains

The actual r vector was composed of 3N individual electron coordinates. The above equation holds for each of these coordinates. Thus, in summary:

which is just what we wanted to show.

Pancake bonding

π-system radicals may interact with each other in a special way. An actual recombination of the radicals is not possible due to the delocalization in the π-system. But the binding between two such radicals is still a lot stronger than would be expected from pure van-der-Waals interactions. This phenomenon is called "pancake bonding".

There is a new paper out by us, studying this: "Study of the Diradicaloid Character in a Prototypical Pancake-Bonded Dimer: The Stacked Tetracyanoethylene (TCNE) Anion Dimer and the Neutral K₂TCNE₂ Complex" in ChemPhysChem.

Pancake bonding is quite demanding from a computational point of view, since you need to describe the static correlation of the radicals as well as dynamic correlation, which determines the dispersion interaction. We used the multireference averaged quadratic coupled cluster (MR-AQCC) method, which should be able to deal with these effects. MR-AQCC is very similar to multireference configuration interaction only that there is an additional correction for size-extensivity.

Ubuntu vs Windows 8

It is quite amazing how much trouble we had with Windows 8. We just got this new Asus Netbook (F201E). The pre-installed Windows 8 was not only completely non-intuitive to use, but so slow that we were close to just throwing the thing out of the window. The task manager showed that there were some processes running all the time on 50% CPU using up hundreds of megabytes RAM. Maybe you can get away with something like that on a workstation if it has multiple cores and lots of RAM. But it was defnitly the wrong thing for our netbook.

What fixed it? Ubuntu. That was my task for yesterday, which went really smooth. Just download the distribution. Then you need to create a bootable USB stick. Tweak the BIOS a little bit to make sure it reads the stick (activate CSM, deactivate SecureBoot). And even the Wifi worked pretty much right away (after I installed the updates).

And now everything runs smooth and as quick as you'd expect a modern computer to work (even if it's a low-end machine).