Dimensionality effects in the electronic structure of organic semiconductors consisting of polar repeat units

In conjugated organic molecules, excitation gaps typically decrease reciprocally with increasing the number of repeat units, n. This usually holds for individual molecules as well as for the corresponding bulk materials. Here, we show using density-functional theory calculations that a qualitatively different evolution is found for layers built from molecules consisting of polar repeat units. Whereas a 1/n-dependence is still observed in the case of isolated polar molecules, the global gap decreases essentially linearly with n in the corresponding 2D-periodic systems and vanishes beyond a certain molecular length, with the frontier states being localized at opposite ends of the layer. The latter is accompanied by a saturation of the dipole moment per molecule, an effect not observed in the isolated polar molecules. Interestingly, in both cases the limit of the gap for long (but finite) molecules differs qualitatively from that of infinite length obtained in 1D-periodic and 3D-periodic calculations, the latter serving as models for polymers and the bulk. We rationalize these dimensionality effects as a consequence of the potential gradient within the finite-length layers. They arise from the collective action of intra-molecular dipoles in the 2D periodic layers and can be traced back to surface effects.