One of the fundamental goals of nanotechnology is to exploit selective and directional interactions between molecules to design particles that self-assemble into desired structures, from capsids, to nano-clusters, to fully formed crystals with target properties (e.g. optical, mechanical, etc.). Here we provide a general framework which transforms the inverse problem of self-assembly of colloidal crystals into a Boolean satisfiability problem for which solutions can be found numerically. Given a reference structure and the desired number of components, our approach produces designs for which the target structure is an energy minimum, and also allows to exclude solutions that correspond to competing structures. We demonstrate the effectiveness of our approach by designing model particles that spontaneously nucleate milestone structures such as the cubic diamond, the pyrochlore and the clathrate lattices.
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