These days many people are interested in polyaromatic hydrocarbons because of their special electronic structure properties, such as reduction of the band gap, spin-polarization, and radical formation. The problem is that precisely these properties make computations on these systems very challenging. Previously, we have studied polyaromatic hydrocarbons with expensive correlated multireference methods. These methods do not only burn lots of computer time but they also require experts for their successful setup and interpretation. The idea of our newest work was to evaluate a very simple model based on Hückel theory and evaluate how this performs in comparison to high-level methods. The results are shown in the paper "

Evaluation of the quasi correlated tight-binding (QCTB) model for describing polyradical character in polycyclic hydrocarbons" that just appeared in J. Chem. Phys.

Amazingly, the new method provides a semi-quantitative reproduction of the ab initio results in the cases we studied. Below, you can find a comparison the ab initio AQCC method with the QCTB model evaluated here. We are comparing polyacenes with isomeric phenacenes. It is well-known that the polyacenes become unstable with longer chain length, obtaining polyradical character, while the phenacenes remain stable. To evaluate this phenomenon, we compute an effectively number of unpaired electrons. Both methods, correctly predict that the unpaired electrons go up of the acenes and stay more or less constant for the phenacenes. But even more: there is a semi-quantiative agreement of the precise values.

The agreement between the two methods is quite amazing considering how much cheaper the QCTB method is. Because of this computational efficiency the QCTB method can even treat graphene nanosheets with thousands of atoms without significant computational cost. Below, the unpaired density for a "perforated" nanoribbon is shown.

Currently, the code is only available in a local Mathematica file. But I might add it as an addition to my

Hückel program, at least a light version.