Calculation of the surface free energy (SFE) is an important application of the thermodynamic integration (TI) methodology, which was mainly employed for atomic crystals (such as Lennard-Jones or metals). In this work, we present the calculation of the SFE of a molecular crystal using the cleaving technique which we implemented in the LAMMPS molecular dynamics package. We apply this methodology to a crystal of β-d-mannitol at room temperature and report the results for two types of force fields belonging to the GROMOS family: all atoms and united atoms. The results show strong dependence on the type of force field used, highlighting the need for the development of better force fields to model the surface properties of molecular crystals. In particular, we observe that the united-atoms force field, despite its higher degree of coarse graining compared to the all-atoms force field, produces SFE results in better agreement with the experimental results from inverse gas chromatography measurements.