1 research outputs found
Entropic trust region for densest crystallographic symmetry group packings
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 -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
its behaviour and performance on various densest packings of convex polygons in
-dimensional CSGs for which optimal solutions are known. Additionally, we
demonstrate the application of the densest CSG packings in the pentacene
thin-film CSP