In ab initio calculations a finite graphitic cluster model is often used to approximate the interaction energy of a water molecule with an infinite single-layer graphitic surface (graphene). In previous studies, the graphitic cluster model is a collection of fused benzene rings terminated by hydrogen atoms. In this study, the effect of using fluorine instead of hydrogen atoms for terminating the cluster model is examined to clarify the role of the boundary. The interaction energy of a water molecule with the graphitic cluster was computed using ab initio methods at the MP2 level of theory and with the 6-31G(d) 0.25) basis set. The interaction energy of a water molecule with graphene is estimated by extrapolation of two series of increasing size graphitic cluster models ((C6nH6n)-H-2 and (C6nF6n)-F-2, n) 1-3). Two fixed orientations of water molecule are considered: ( a) both hydrogen atoms of water pointing toward the cluster (mode A) and (b) both hydrogen atoms of water pointing away from the cluster (mode B). The interaction energies for water mode A are found to be -2.39 and -2.49 kcal/mol for (C6nH6n)-H-2 and (C6nF6n)-F-2 cluster models, respectively. For water mode B, the interaction energies are -2.32 and -2.44 kcal/mol for (C6nH6n)-H-2 and (C6nF6n)-F-2 cluster models, respectively.