Motivated by an experiment in which the singlet-triplet gap in triphenylene based copolymers was effectively tuned, we used time dependent density functional theory (TDDFT) to reproduce the main results. By means of conventional and long-range correc
ted exchange correlation functionals, the luminescence energies and the exciton localization were calculated for a triphenylene homopolymer and several different copolymers. The phosphorescence energy of the pure triphenylene chain is predicted accurately by means of the optimally tuned long-range corrected LC-PBE functional and slightly less accurate by the global hybrid B3LYP. However, the experimentally observed fixed phosphorescence energy could not be reproduced because the localization pattern is different to the expectations: Instead of localizing on the triphenylene moiety - which is present in all types of polymers - the triplet state localizes on the different bridging units in the TDDFT calculations. This leads to different triplet emission energies for each type of polymer. Yet, there are clear indications that long-range corrected TDDFT has the potential to predict the triplet emission energies as well as the localization behavior more accurate than conventional local or semi-local functionals.
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be numerically
stable for a wide range of geometrical parameters and momenta. Details of the implementation are presented together with benchmark data for representative integrals. We also discuss the assets and drawbacks of alternative algorithms available and analyze the numerical efficiency of the new scheme.
