Inverse design of isotropic pair potentials using digital alchemy with a generalized Fourier potential

Advances in synthesizing colloidal nanoparticles with tailored interactions through surface modifications provide vast possibilities to create new materials through self-assembly. Alongside experimental advances, computational methods are contributing to rational materials-by-design by inversely optimizing building blocks capable of self-assembling into target structures. Radially symmetric (isotropic) pair potentials are commonly used to model interacting particles in such a design process. In this work, we apply an inverse design approach called ‘digital alchemy’ to a generalized Fourier potential (FP) to search a broad design space of isotropic pair interactions targeting 23 crystal structures spanning a range of complexities. Digital alchemy (DA) is a method for optimizing nanoparticle attributes (such as interaction strength and range, and even particle shape) for a target structure in a generalized thermodynamic framework where the attributes are treated as fluctuating thermodynamic variables in situ. Using DA, we find six optimized isotropic interaction potentials that produce six corresponding targeted crystal structures via self-assembly. Importantly, these six are those cases where the optimized potential for the target structure and the ground state structure at zero temperature for the corresponding potential coincide. In these cases, the optimized pair potential is the “best” potential for the crystal structure and the crystal structure is, conversely, the “best” structure for the pair potential. For other cases, we show that although most of the optimized isotropic pair potentials stabilize their corresponding target structures, the structures do not self-assemble when the target structure has structurally similar polymorphs. In such cases, we obtain a family of nearly identical optimized potentials for the set of similar structures, and only one of them—the structure that minimizes the energy (i.e. is “best”) for the obtained potential—can be successfully self-assembled. We discuss and provide insight into these limitations inherent in using isotropic pair potentials for inverse design. Graphic abstract