TDDFT for large conjugated systems

About five years ago, when we tried applying TDDFT to large conjugated systems, we noticed that it just did not work. This confused me for a while: What is so difficult about conjugated systems? Then I searched the literature, which showed that other people noticed the same problem quite a while ago (e.g. S. Grimme), that the phenomenon was interpreted in terms of exciton sizes, and that it was seen as "charge transfer in disguise." The thing that was still missing was a tangible way to analyze and talk about this problem. Therefore, we wanted to look at it from a somewhat different viewpoint. We took a set of conjugated polymers of varying sizes, performed TDDFT computations with different functionals, and analyzed the computations with our wavefunction analysis toolbox for TDDFT. The results are shown in our paper "Universal Exciton Size in Organic Polymers is Determined by Nonlocal Orbital Exchange in Time-Dependent Density Functional Theory" in JPCL.

The main quantity we are interested in is the exciton size, which corresponds to a dynamic charge transfer distance. The first striking observation is that the exciton size is largely independent of the molecular details but scales uniformly with the system size, as initially pointed out by Knupfer et al. The second point, important from a methodological point of view, is that huge variations between the functionals are observed. A bound exciton can only be formed if non-local exchange is included in the functional. The more non-local exchange is included, the stronger the observed binding.