  In this work, we systematically investigate the singly-charmed pentaquark
molecular states $D^{(*)}N$, $D^{(*)}\Xi^{(*)}$ and $D_s^{(*)}\Xi^{(*)}$ with
the QCD sum rules by carrying out the operator product expansion up to the
vacuum condensates of dimension 13 and taking fully account of the light-flavor
$SU(3)$ breaking effects. The numerical results favor assigning the
$\Omega_c(3185)$ as the $D\Xi$ molecular state with the $J^P=\frac{1}{2}^-$ and
$| I,I_3 \rangle=| 0,0 \rangle$, assigning the $\Omega_c(3327)$ as the $D^*\Xi$
molecular state with the $J^P=\frac{3}{2}^-$ and $|I,I_3 \rangle=| 0,0
\rangle$, assigning the $\Sigma_c(2800)$ as the $DN$ molecular state with the
$J^P=\frac{1}{2}^-$ and $| I,I_3 \rangle=| 1,0 \rangle$, and assigning the
$\Lambda_c(2940)/\Lambda_c(2910)$ as the $D^*N$ molecular state with the
$J^P=\frac{3}{2}^-$ and $| I,I_3 \rangle=| 0,0 \rangle$. Other potential
molecule candidates are also predicted, which may be observed in future
experiments. For example, we can search for the $D\Xi$ and $D^*\Xi$ molecular
states with the isospin $| I,I_3 \rangle=| 1,\pm1 \,\rangle$ in the
$\Xi_c^+\bar{K}^0$ and $\Xi_c^0\bar{K}^-$ mass spectrum respectively in the
future, which could shed light on the nature of the $\Omega_c(3185/3327)$.
