  The charmed $ \Lambda_{c}^{+} $ hypernuclei are investigated within the
framework of the density-dependent relativistic mean-field (DDRMF) theory.
Starting from the empirical hyperon potential in symmetric nuclear matter,
obtained through microscopic first-principle calculations, two sets of
$\Lambda_c N$ effective interactions were derived by fitting the potentials
with minimal uncertainty (Fermi momentum $k_{F,n} = 1.05~\rm{fm}^{-1}$) and
near saturation density ($k_{F,n} = 1.35~\rm{fm}^{-1}$). These DDRMF models
were then used to explore the $\Lambda_{c} N$ effective interaction
uncertainties on the description of hypernuclear bulk and single-particle
properties. A systematic investigation was conducted on the existence of bound
$\Lambda_{c}^{+}$ hypernuclei. The dominant factors affecting the existence and
stability of hypernuclei were analyzed from the perspective of the
$\Lambda_{c}^{+}$ potential. It is found that the hyperon potential is not only
influenced by the Coulomb repulsion, but by an extra contribution from the
rearrangement terms due to the density dependence of the meson-baryon coupling
strengths. Therefore, the rearrangement term significantly impacts the
stability description for light hypernuclei, while for heavier hypernuclei, the
contribution from Coulomb repulsion becomes increasingly significant and
eventually dominant. The discussion then delves into the bulk and
single-particle properties of charmed hypernuclei using these models. It is
found that even when different models yield similar hyperon potentials for
nuclear matter, different treatments of nuclear medium effects could lead to
disparities in the theoretical description of hypernuclear structures. This
study indicates that constraints on the $ \Lambda_{c} N $ interaction at finite
densities are crucial for the study of $ \Lambda_{c}^{+} $ hypernuclear
structures.
