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Interactions between planar Cu phthalocyanine molecules, CuPc, arranged in vertical stacking sequence are studied by first-principles density functional (DF) and semiempirical molecular dynamics (MD) methods. Dependence of electronic structure upon interplanar spacing and staggering angle is analyzed in order to interpret observed electrical conductivity and magnetic coupling behavior of partially oxidized Cu(pc)I. MD predictions of equilibrium structure of dimers and tetramers are in excellent agreement with experiment on the linear chain species. DF predictions of interaction energy of dimers are compared with MD and experiment.