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We perform a systematic study of the possible loosely bound states composedof two charmed baryons or a charmed baryon and an anti-charmed baryon withinthe framework of the one boson exchange (OBE) model. We consider not only the$\pi$ exchange but also the $\eta$, $\rho$, $\omega$, $\phi$ and $\sigma$exchanges. The $S-D$ mixing effects for the spin-triplets are also taken intoaccount. With the derived effective potentials, we calculate the bindingenergies and root-mean-square (RMS) radii for the systems$\Lambda_c\Lambda_c(\bar{\Lambda}_c)$, $\Xi_c\Xi_c(\bar{\Xi}_c)$,$\Sigma_c\Sigma_c(\bar{\Sigma}_c)$,$\Xi_c^\prime\Xi_c^\prime(\bar{\Xi}_c^\prime)$ and$\Omega_c\Omega_c(\bar{\Omega}_c)$. Our numerical results indicate that: (1)the H-dibaryon-like state $\Lambda_c\Lambda_c$ does not exist; (2) there mayexist four loosely bound deuteron-like states $\Xi_c\Xi_c$ and$\Xi_c^\prime\Xi_c^\prime$ with small binding energies and large RMS radii.

Possible Deuteron-like Molecular States Composed of Heavy Baryons