  We study $D_s^+ D_s^-$ and $D \bar D$ states assuming that they are hadronic
molecules with $J^{PC}=0^{++}$ quantum number. We use two-point QCD sum rule
formalism and extract the mass and decay constant values of these states. We
take into account contributions of various quark, gluon, and mixed vacuum
condensates up to dimension eight. The extracted mass and decay constant values
of $D \bar D$ and $D_s^+ D_s^-$ states read as $M_{D \bar D} = 3795^{+85}_{-82}
~\mathrm{MeV} $, $f_{D \bar D} = 1.70^{+0.33}_{-0.29} \times 10^{-2}
~\mathrm{GeV}^5$, and $M_{D_s^+ D_s^-} = 3983^{+93}_{-88} ~\mathrm{MeV}$,
$f_{D_s^+ D_s^-} = 2.52^{+0.64}_{-0.54} \times 10^{-2} ~\mathrm{GeV}^5$,
respectively. The predicted mass of $D_s^+ D_s^-$ state is in good agreement
with the recent LHCb observation and supports quantum number and molecular
picture assignments. A possible observation of $D \bar D$ state would help for
establishing the lowest four-quark state in charmonium sector.
