Determination of optimal potential parameters for the self-assembly of various lattice structures

We present a gradient-based optimization method that precisely designs simplified isotropic potentials for self-assembly of targeted lattice structures. An ansatz potential and its constraints are constructed to directly reflect the characteristics of a Bravais lattice for the target crystal, and the method is able to design the simplified potential systematically and smoothly. The potential is simplified with a Gaussian function in reciprocal space to minimize the information loss caused by Fourier transform in each design update. Design optimization formulation is derived using design sensitivity to relative entropy, employing a Fourier-Filtered Relative Entropy Minimization (FF-REM) formulation embedded in LAMMPS code to be used as an optimization tool. The potential obtained through this optimization method can successfully self-assemble low-coordinated crystals, such as square, triangle, honeycomb, and Kagome lattices, without further smoothing techniques. It turns out that completely removing the competitive alternative structures is an important condition for improving stability in self-assembling the target lattice in various density ranges.