Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
J Chem Phys. 2018 Nov 28;149(20):204102. doi: 10.1063/1.5063802.
The synthesis of complex materials through the self-assembly of particles at the nanoscale provides opportunities for the realization of novel material properties. However, the inverse design process to create experimentally feasible interparticle interaction strategies is uniquely challenging. Standard methods for the optimization of isotropic pair potentials tend toward overfitting, resulting in solutions with too many features and length scales that are challenging to map to mechanistic models. Here we introduce a method for the optimization of simple pair potentials that minimizes the relative entropy of the complex target structure while directly considering only those length scales most relevant for self-assembly. Our approach maximizes the relative information of a target pair distribution function with respect to an ansatz distribution function via an iterative update process. During this process, we filter high frequencies from the Fourier spectrum of the pair potential, resulting in interaction potentials that are smoother and simpler in real space and therefore likely easier to make. We show that pair potentials obtained by this method assemble their target structure more robustly with respect to optimization method parameters than potentials optimized without filtering.
通过纳米尺度颗粒的自组装合成复杂材料为实现新型材料性能提供了机会。然而，创建可在实验中实现的颗粒间相互作用策略的逆向设计过程极具挑战性。各向同性对势优化的标准方法往往会出现过拟合，导致解决方案具有太多特征和长度尺度，难以映射到机械模型。在这里，我们引入了一种优化简单对势的方法，该方法可以在最小化复杂目标结构的相对熵的同时，仅直接考虑对自组装最相关的那些长度尺度。我们的方法通过迭代更新过程，使目标对分布函数相对于假设分布函数的相对信息最大化。在这个过程中，我们从对势的傅里叶谱中过滤高频，得到在实空间中更平滑、更简单的相互作用势，因此更容易实现。我们表明，与未过滤的对势相比，通过这种方法获得的对势在优化方法参数方面更能稳定地组装目标结构。
