Inverse design of two-dimensional structure by self-assembly of patchy particles

We propose an optimization method for the inverse structural design of self-assembly of anisotropic patchy particles. The anisotropic interaction can be expressed by the spherical harmonics of the surface pattern on a patchy particle, and thus, arbitrary symmetries of the patch can be treated. The pairwise interaction potential includes several to-be-optimized parameters, which are the coefficients of each term in the spherical harmonics. We use the optimization method based on the relative entropy approach and generate structures by Brownian dynamics simulations. Our method successfully estimates the parameters in the potential for the target structures, such as square lattice, kagome lattice, and dodecagonal quasicrystal.