All-atom simulations are used to derive effective parameters for a coarse-grained description of the crystalline cellulose Ia. In this description, glucose monomers are represented by the C4 atoms and non-bonded interactions within the cellulose sheets and between the sheets by effective LennardJones interactions. The parameters are determined by two methods: the Boltzmann inversion and through monitoring of the energies associated with changes of the coarse-grained degrees of freedom. We find that the stiffness-related parameters for cellulose Ia are nearly the same as for Ib allomorph. However, the non-bonded terms are placed differently and are weaker leading to an overall lower energy, and free energy, of Ib compared to Ia. We apply the coarsegrained description to determine amorphous transition states for the room-temperature conversion process between the Ia and Ib allomorphs and to characterize the interface between the crystalline forms of the allomorphs.