  We calculate the uniaxial and dilatation acoustic deformation potentials,
$\Xi^{\text{L}}_{u}$ and $\Xi^{\text{L}}_{d}$, of the conduction band L valleys
of PbTe from first principles, using the local density approximation (LDA) and
hybrid functional (HSE03) exchange-correlation functionals. We find that the
choice of a functional does not substantially affect the effective band masses
and deformation potentials as long as a physically correct representation of
the conduction band states near the band gap has been obtained. Fitting of the
electron-phonon matrix elements obtained in density functional perturbation
theory (DFPT) with the LDA excluding spin orbit interaction (SOI) gives
$\Xi^{\text{L}}_u = 7.0$~eV and $\Xi^{\text{L}}_d = 0.4$~eV. Computing the
relative shifts of the L valleys induced by strain with the HSE03 functional
including SOI gives $\Xi^{\text{L}}_u = 5.5$~eV and $\Xi^{\text{L}}_d =
0.8$~eV, in good agreement with the DFPT values. Our calculated values of
$\Xi^{\text{L}}_u$ agree fairly well with experiment ($\sim 3-4.5$~eV). The
computed values of $\Xi^{\text{L}}_d$ are substantially smaller than those
obtained by fitting electronic transport measurements ($\sim 17-22$~eV),
indicating that intravalley acoustic phonon scattering in PbTe is much weaker
than previously thought.
