  Starting with the early alchemists, a holy grail of science has been to make
desired materials by modifying the attributes of basic building blocks.
Building blocks that show promise for assembling new complex materials can be
synthesized at the nanoscale with attributes that would astonish the ancient
alchemists in their versatility. However, this versatility means that making
direct connection between building block attributes and bulk behavior is both
necessary for rationally engineering materials, and difficult because building
block attributes can be altered in many ways. Here we show how to exploit the
malleability of the valence of colloidal nanoparticle "elements" to directly
and quantitatively link building block attributes to bulk behavior through a
statistical thermodynamic framework we term "digital alchemy". We use this
framework to optimize building blocks for a given target structure, and to
determine which building block attributes are most important to control for
self assembly, through a set of novel thermodynamic response functions, moduli
and susceptibilities. We thereby establish direct links between the attributes
of colloidal building blocks and the bulk structures they form. Moreover, our
results give concrete solutions to the more general conceptual challenge of
optimizing emergent behaviors in nature, and can be applied to other types of
matter. As examples, we apply digital alchemy to systems of truncated
tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that
self assemble diamond, FCC, and icosahedral quasicrystal structures,
respectively.
