The energy scale of interactions that control molecular adsorption and assembly on surfaces can vary by several orders of magnitude, yet the importance of each contributing interaction is not apparent a-priori.Tetracyanoquinodimethane (TCNQ) is an archetypal electron acceptor molecule and it is a key component of organic metals. On metal surfaces, this molecule also acts as an electron acceptor, producing negatively charged adsorbates. It is therefore rather intriguing to observe attractive molecular interactions in this system that was reported previously for copper and silver surfaces. Our experiments compared TCNQ adsorption on noble metal surfaces of Ag(100) and Ag(111). In both cases we found net attractive interactions down to the lowest coverage. However, the morphology of the assemblies was strikingly different, with 2D islands on Ag(100) and 1D chains on Ag(111) surfaces. This observation suggests that the registry effect governed by the molecular interaction with the underlying lattice potential is critical in determining the dimensionality of the molecular assembly. Using first-principles 2 density functional calculations with van der Waals correction scheme, we revealed that the strengths of major interactions (i.e., lattice potential corrugation, intermolecular attraction, and charge transferinduced repulsion) are all similar in energy. Van der Waals interactions, in particular, almost double the strength of attractive interactions, making the intermolecular potential comparable in strength to the diffusion potential and promoting self-assembly. However, it is the anisotropy of local intermolecular interactions that is primarily responsible for the difference in the topology of the molecular islands on Ag(100) and Ag(111) surfaces. We anticipate that the intermolecular potential will become more attractive and dominant over the diffusion potential with increasing molecular size, providing new design strategies for the structure and charge-transfer within molecular layers.