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Molecular crystal structure prediction (CSP) seeks the most stable periodicstructure given the chemical composition of a molecule and pressure-temperatureconditions. Modern CSP solvers use global optimization methods to search forstructures with minimal free energy within a complex energy landscape inducedby intermolecular potentials. A major caveat of these methods is that initialconfigurations are random, making thus the search susceptible to convergence atlocal minima. Providing initial configurations that are densely packed withrespect to the geometric representation of a molecule can significantlyaccelerate CSP. Motivated by these observations, we define a class of periodicpackings restricted to crystallographic symmetry groups (CSG) and design asearch method for the densest CSG packings in an information-geometricframework. Since the CSG induce a toroidal topology on the configuration space,a non-Euclidean trust region method is performed on a statistical manifoldconsisting of probability distributions defined on an $n$-dimensional flat unittorus by extending the multivariate von Mises distribution. Introducing anadaptive quantile reformulation of the fitness function into the optimizationschedule provides the algorithm with a geometric characterization through localdual geodesic flows. Moreover, we examine the geometry of the adaptiveselection-quantile defined trust region and show that the algorithm performs amaximization of stochastic dependence among elements of the extendedmultivariate von Mises distributed random vector. We experimentally evaluatethe behavior and performance of the method on various densest packings ofconvex polygons in $2$-dimensional CSGs for which optimal solutions are known,and demonstrate its application in the pentacene thin-film CSP.

Entropic trust region for densest crystallographic symmetry group packings