  The properties of hydrogen at warm dense matter (WDM) conditions are of high
importance for the understanding of astrophysical objects and technological
applications such as inertial confinement fusion. In this work, we present
extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the
electronic properties in the Coulomb potential of a fixed ionic configuration.
This gives us new insights into the complex interplay between the electronic
localization around the protons with their density response to an external
harmonic perturbation. We find qualitative agreement between our simulation
data and a heuristic model based on the assumption of a local uniform electron
gas model, but important trends are not captured by this simplification. In
addition to being interesting in their own right, we are convinced that our
results will be of high value for future projects, such as the rigorous
benchmarking of approximate theories for the simulation of WDM, most notably
density functional theory.
