  We consider electron(hole)-phonon coupling in crystalline organic
semiconductors, using naphthalene for our case study. Employing a
first-principles approach, we compute the changes in the self-consistent
Kohn-Sham potential corresponding to different phonon modes and go on to obtain
the carrier-phonon coupling matrix elements (vertex functions). We then
evaluate perturbatively the quasiparticle spectral residues for electrons at
the bottom of the lowest-unoccupied- (LUMO) and holes at the top of the
highest-occupied (HOMO) band, respectively obtaining $Z_e\approx 0.74$ and
$Z_h\approx 0.78$. Along with the widely accepted notion that the
carrier-phonon coupling strengths in polyacenes decrease with increasing
molecular size, our results provide a strong microscopic evidence for the
previously conjectured nonpolaronic nature of band-like carriers in these
systems.
