  In this article, we construct the six-quark currents with the $J^P=0^+$,
$0^-$, $1^+$ and $1^-$ to study the $\Lambda_c$$\Lambda_c$ dibaryon and
$\Lambda_c$$\bar{\Lambda}_c$ baryonium states via QCD sum rules. We consider
the vacuum condensates up to dimension 16 and truncation of the order
$\mathcal{O}(\alpha_s^k )$ with $k\leq3$. The predicted masses are
$5.11_{-0.12}^{+0.15}$GeV, $4.66_{-0.06}^{+0.10}$GeV, $4.99_{-0.09}^{+0.10}$GeV
$4.68^{+0.08}_{-0.08}$GeV for the $J^P=0^+$, $0^-$, $1^+$ and $1^-$ states,
respectively, which can be confronted to the experimental data in the future
considering the high integrated luminosity at the center-of-mass energy about
$4.8\,\rm{GeV}$ at the BESIII. We find the terms with $\frac{3}{2}< k \leq 3$
do play a tiny role, and we can ignore these terms safely in the QCD sum rules.
