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We use inverse methods of statistical mechanics and computer simulations toinvestigate whether an isotropic interaction designed to stabilize a giventwo-dimensional (2D) lattice will also favor an analogous three-dimensional(3D) structure, and vice versa. Specifically, we determine the 3D orderedlattices favored by isotropic potentials optimized to exhibit stable 2Dhoneycomb (or square) periodic structures, as well as the 2D ordered structuresfavored by isotropic interactions designed to stabilize 3D diamond (or simplecubic) lattices. We find a remarkable `transferability' of isotropic potentialsdesigned to stabilize analogous morphologies in 2D and 3D, irrespective of theexact interaction form, and we discuss the basis of this cross-dimensionalbehavior. Our results suggest that the discovery of interactions that driveassembly into certain 3D periodic structures of interest can be assisted byless computationally intensive optimizations targeting the analogous 2Dlattices.

Dimensionality and design of isotropic interactions that stabilize honeycomb, square, simple cubic, and diamond lattices