Molecular crystal structure prediction (CSP) seeks the most stable periodic structure given the chemical composition of a molecule and pressure-temperature conditions. Modern CSP solvers use global optimization methods to search for structures with minimal free energy within a complex energy landscape induced by intermolecular potentials. A major caveat of these methods is that initial configurations are random, making thus the search susceptible to convergence at local minima. Providing initial configurations that are densely packed with respect to the geometric representation of a molecule can significantly accelerate CSP. Motivated by these observations, we define a class of periodic packings restricted to crystallographic symmetry groups (CSG) and design a search method for the densest CSG packings in an information-geometric framework. Since the CSG induce a toroidal topology on the configuration space, a non-Euclidean trust region method is performed on a statistical manifold consisting of probability distributions defined on an $n$-dimensional flat unit torus by extending the multivariate von Mises distribution. Introducing an adaptive quantile reformulation of the fitness function into the optimization schedule provides the algorithm with a geometric characterization through local dual geodesic flows. Moreover, we examine the geometry of the adaptive selection-quantile defined trust region and show that the algorithm performs a maximization of stochastic dependence among elements of the extended multivariate von Mises distributed random vector. We experimentally evaluate the behavior and performance of the method on various densest packings of convex polygons in $2$-dimensional CSGs for which optimal solutions are known, and demonstrate its application in the pentacene thin-film CSP.

翻译：分子晶体结构预测（CSP）旨在根据分子的化学组成及压力-温度条件，寻找最稳定的周期性结构。现代CSP求解器采用全局优化方法，在由分子间势能诱导的复杂能量景观中搜索自由能最小的结构。这些方法的一个主要缺陷在于初始构型是随机的，导致搜索易收敛于局部极小值。提供与分子几何表示紧密堆积的初始构型可显著加速CSP。基于这些观察，我们定义了一类受限于晶体学对称群（CSG）的周期性堆积，并在信息几何框架下设计了最密CSG堆积的搜索方法。由于CSG在构型空间上诱导出环面拓扑，我们通过在$n$维平坦单位环面上扩展多变量冯·米塞斯分布，在由概率分布构成的统计流形上执行非欧几里得置信域方法。将适应度函数的自适应分位数重构引入优化调度后，算法通过局部对偶测地流获得了几何表征。我们还分析了自适应选择-分位数定义的置信域的几何性质，并证明该算法实现了扩展多变量冯·米塞斯分布随机向量元素间随机依赖性的最大化。我们针对已知最优解的二维CSG中凸多边形最密堆积问题，实验评估了该方法的性能与行为，并展示了其在并五苯薄膜CSP中的应用。