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We follow the evolution of the Ionization Potential (IP) for the paradigmaticquasi-one-dimensional trans-acetylene family of conjugated molecules, fromshort to long oligomers and to the infinite polymer trans-poly-acetylene (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 givenvalue for TPA with a smooth, coupled inverse-length-exponential behavior. Ourprediction is based on an "internally-consistent" scheme to adjust the exchangemixing parameter $\alpha$ of the PBEh hybrid density functional, so as toobtain a description of the electronic structure consistent with thequasiparticle approximation for the IP. This is achieved by demanding that thecorresponding quasiparticle correction, in the GW@PBEh approximation, vanishesfor the IP when evaluated at PBEh($\alpha^{ic}$). We find that $\alpha^{ic}$ isalso system-dependent and converges with increasing oligomer length, allowingto capture the dependence of IP and other electronic properties.

Length Dependence of Ionization Potentials of Trans-Acetylenes: Internally-Consistent DFT/GW Approach