  We present an analysis of the static exchange-correlation (XC) kernel
computed from hybrid functionals with a single mixing coefficient such as PBE0
and PBE0-1/3. We break down the hybrid XC kernels into the exchange and
correlation parts using the Hartree-Fock functional, the exchange-only PBE, and
the correlation-only PBE. This decomposition is combined with exact data for
the static XC kernel of the uniform electron gas and an Airy gas model within a
subsystem functional approach. This gives us a tool for the nonempirical choice
of the mixing coefficient at ambient and extreme conditions. Our analysis
provides physical insights into the effect of the variation of the mixing
coefficient in hybrid functionals, which is of immense practical value. The
presented approach is general and can be used for other type of functionals
like screened hybrids.
