Role of localization in optimal tuning: From monomers to polymers.

Optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting fundamental gaps, initially for molecules and more recently also for band gaps of solid-state systems. Application to solids is based on an extension of the ionization potential theorem, an exact physical condition, to an ansatz that generalizes it to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials throughout the evolution of the chain length.