  Kohn-Sham DFT with optimally tuned range-separated hybrid (RSH) functionals
provides accurate and nonempirical fundamental gaps for a wide variety of
finite-size systems. The standard tuning procedure relies on calculation of
total energies of charged systems and thus cannot be applied to periodic
solids. Here, we develop a framework for tuning the range separation parameter
that can be used for periodic and open boundary conditions. The basic idea is
to choose the range parameter that results in a stationary point where the
fundamental gap obtained by RSH matches the gap obtained from a G0W0 over RSH
calculation. The proposed framework is therefore analogous to eigenvalue
self-consistent GW (scGW). We assess the method for various solids and obtain
very good agreement with scGW results.
