  The ionization potential of molecular chains is well-known to be a tunable
nano-scale property that exhibits clear quantum confinement effects.
State-of-the-art methods can accurately predict the ionization potential in the
small molecule limit and in the solid-state limit, but for intermediate,
nano-sized systems prediction of the evolution of the electronic structure
between the two limits is more difficult. Recently, optimal tuning of
range-separated hybrid functionals has emerged as a highly accurate method for
predicting ionization potentials. This was first achieved for molecules using
the ionization potential theorem (IPT) and more recently extended to
solid-state systems, based on an \textit{ansatz} that generalizes the IPT 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 using this approach. 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 for any chain length, including the
nano-scale regime.
