  A simple effective screening parameter for screened range-separated hybrid is
constructed from the compressibility sum rule in the context of linear-response
time-dependent Density Functional Theory. When applied to the
dielectric-dependent hybrid (DDH), it becomes remarkably accurate for bulk
solids compared to those obtained from fitting with the model dielectric
function or depending on the valence electron density of materials. The present
construction of the screening parameter is simple and realistic. The screening
parameter developed in this way is physically appealing and practically useful
as it is straightforward to obtain using the average over the unit cell volume
of the bulk solid, bypassing high-level calculations of the dielectric function
depending on random-phase approximation. Furthermore, we have obtained a very
good accuracy for energy band gaps, positions of the occupied d-bands,
ionization potentials, optical properties of semiconductors and insulators, and
geometries of bulk solids (equilibrium lattice constants and bulk moduli) from
the constructed DDH.
