  Consistency between the exchange-correlation (xc) functional used during
pseudopotential construction and planewave-based electronic structure
calculations is important for an accurate and reliable description of the
structure and properties of condensed-phase systems. In this work, we present a
general scheme for constructing pseudopotentials with range-separated hybrid
(RSH) xc functionals based on the solution of the all-electron radial
integro-differential equation for a spherical atomic configuration. As
proof-of-principle, we demonstrate pseudopotential construction with the PBE,
PBE0, HSE, and sRSH (based on LC-$\omega$PBE0) xc functionals for a select set
of atoms, and then investigate the importance of pseudopotential consistency
when computing band gaps, equilibrium lattice parameters, bulk moduli, and
atomization energies of several solid-state systems. In doing so, we find that
pseudopotential consistency errors (PSCE) tend to be systematic and can be as
large as $1.4\%$ when computing these properties.
