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We report a systematic study of the weak chemical bond between two benzenemolecules. We first show that it is possible to obtain a very good descriptionof the C_2 dimer and the benzene molecule, by using pseudopotentials for thechemically inert 1s electrons, and a resonating valence bond wave function as avariational ansatz, expanded on a relatively small Gaussian basis set. Weemploy an improved version of the stochastic reconfiguration technique tooptimize the many-body wave function, which is the starting point for highlyaccurate simulations based on the lattice regularized diffusion Monte Carlo(LRDMC) method. This projection technique provides a rigorous variational upperbound for the total energy, even in the presence of pseudopotentials, andallows to improve systematically the accuracy of the trial wave function, whichalready yields a large fraction of the dynamical and non-dynamical electroncorrelation. We show that the energy dispersion of two benzene molecules in theparallel displaced geometry is significantly deeper than the face-to-faceconfiguration. However, contrary to previous studies based on post Hartree-Fockmethods, the binding energy remains weak (~ 2 kcal/mol) also in this geometry,and its value is in agreement with the most accurate and recent experimentalfindings.Comment: 12 pages, 6 figures, submitted to the Journal of Chemical Physic

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods