  Stimulated by the observation of the newly $X(3960)$ observed by the LHCb
collaboration, we adopt the one-boson-exchange model and consider the $S-D$
wave mixing effects to study the $D_s\bar{D}_s/D^*\bar{D}^*/D_s^*\bar{D}_s^*$
interactions with $I(J^{PC})=0(0^{++})$. After producing the phase shifts of
this coupled channel systems, our results show that there can exist a
charmoniumlike resonance, whose obtained mass and width can both well match
with the experimental data of the newly observed $X(3960)$. We also find that
the $D^*\bar{D}^*$ system plays an important role in the formation of the newly
observed $X(3960)$ as a charmoniumlike resonance, and the $D_s^*\bar{D}_s^*$
system makes a significant contribution to the resonant width. As a byproduct,
we perform a coupled channel analysis on the
$D^*\bar{D}^*/D_s\bar{D}_s^*/D_s^*\bar{D}_s^*$ interactions with
$I(J^{PC})=0(1^{+-})$, our results can predict the existence of the
$D_s\bar{D}_s^*$ molecule with $1^{+-}$ and the $D_s^*\bar{D}_s^*$ molecule
with $1^{+-}$. Their widths are around several and several to several tens MeV,
respectively. Experimental searches for these two possible charmoniumlike
molecular candidates can be helpful to verify our proposal.
