  The sensitivity of the PbF molecule to the electron electric dipole moment
has motivated detailed microwave spectroscopy. Previous theoretical approaches
cannot fully explain the spectra. In turn, the explanation from "first
principles" is very important both for molecular theory and for confirmation of
the correctness of the interpretation of experimental data obtained with high
precision. All of these issues are decisively addressed here. We have
determined centrifugal correction parameters for hyperfine structure constants,
both on lead and fluorine nuclei, of the $X^2\Pi_{1/2}$ state of lead
monofluoride. These parameters were obtained by fitting experimentally observed
pure rotational transitions and from {\it ab initio} calculations. We show that
taking this correction into account is required to reproduce the experimental
transition energies obtained in [Phys. Rev. A 84, 022508 (2011)].
