Exciton sizes

When you do not understand the wikipedia article about the very topic you are supposed to be working on, what do you do? Do you ignore this fact, do you give up, or do you see it as a chance?

When I started working on excitons five years ago, I first checked out the wikipedia article, which talked about weird things like exciton binding energies and exciton sizes. An excited state is a transition between orbitals, right? So why would you talk about quasi-particles? Is a "hole" an actual thing and why is it paired with a specific "electron" when you already have tons of electrons floating around?

In a sense my work since then has been occupied with understanding that wikepedia article. It started with our work on excitonic and charge resonance interactions, continued with a series in JCP about analysis and visualization of excited states, went on with the release of the TheoDORE analysis package, and is now finally at a point where we are computing exciton sizes (as demanded by the wikipedia article). The new paper is called "Exciton analysis of many-body wave functions: Bridging the gap between the quasiparticle and molecular orbital pictures" which it appeared yesteday in Phys. Rev. A.

Our idea is to interpret the transition density matrix as an effective exciton wavefunction. This creates a clear rule for computing operator expectation values and reduces the problem to linear algebra. We started with exciton sizes since it is simple to deal with the required multipole integrals. But remembering the wikipedia article, I would also be very interested in the binding energies. All we need for this, is the electron repulsion integrals, which are easily accessible as well. But the physical interpretation is a little bit more difficult because of "screening" (another one of those terms which quantum chemists don't like).

The main area of application will probably be the case of large quasi-periodic systems like conjugated organic polymers where the molecular and the solid-state viewpoints meet. But it is also interesting to look at simple dimers of molecules. In such a case, the exciton size of a charge separated state is equivalent to the distance between the two molecules while it is independent of the distance for locally excited states. Below we are showing this in the case of the pyrdine dimer, considering (a) the excitation energies, (b) the exciton size, and (c) the charge transfer measure that we defined earlier.

The added complication in the case of this system is the symmetry which makes all the states and orbitals delocalized over the whole system and takes away the possibility for net transfer of charge or a dipole moment along the separation direction. As shown above, the states are still divided into excitonic and charge resonance states. The difference between them is the correlation between the electron and hole.