Length dependence of ionization potentials of transacetylenes: Internally consistent DFT/ GW approach

We follow the evolution of the ionization potential (IP) for the paradigmatic quasi-one-dimensional transacetylene family of conjugated molecules, from short to long oligomers and to the infinite polymer transpolyacetylene (TPA). Our results for short oligomers are very close to experimental available data. We find that the IP varies with oligomer length and converges to the given value for TPA with a smooth, coupled inverse-length-exponential behavior. Our prediction is based on an "internally consistent" scheme to adjust the exchange mixing parameter α of the PBEh hybrid density functional, so as to obtain a description of the electronic structure consistent with the quasiparticle approximation for the IP. This is achieved by demanding that the corresponding quasiparticle correction, in the GW@PBEh approximation, vanishes for the IP when evaluated at PBEh(αic). We find that αic is also system-dependent and converges with increasing oligomer length, enabling the dependence of the IP and other electronic properties to be identified.