The role of pressure in inverse design for assembly

Isotropic pairwise interactions that promote the self-assembly of complex particle morphologies have been discovered by inverse design strategies derived from the molecular coarse-graining literature. While such approaches provide an avenue to reproduce structural correlations, thermodynamic quantities such as the pressure have typically not been considered in self-assembly applications. In this work, we demonstrate that relative entropy optimization can be used to discover potentials that self-assemble into targeted cluster morphologies with a prescribed pressure when the iterative simulations are performed in the isothermal-isobaric ensemble. The benefits of this approach are twofold. First, the structure and the thermodynamics associated with the optimized interaction can be controlled simultaneously. Second, by varying the pressure in the optimization, a family of interparticle potentials that all self-assemble the same structure can be systematically discovered, allowing for a deeper understanding of self-assembly of a given target structure and providing multiple assembly routes for its realization. Selecting an appropriate simulation ensemble to control the thermodynamic properties of interest is a general design strategy that could also be used to discover interaction potentials that self-assemble structures having, for example, a specified chemical potential.