Reliable and efficient parameter estimation methodologies for crystal structure prediction

Abstract

Originally borne out of scientific curiosity, Crystal Structure Prediction (CSP) is a rapidly developing area of materials science. The aim of CSP is to predict the crystal structures of a compound given as little information as the molecular connectivity of that compound. This is a task of particular importance due to the prevalence of polymorphism; the possibility that a compound may form different crystalline arrangements in the solid-state. The physico-chemical properties of a compound are intrinsically linked to the polymorph obtained during synthesis. Discovery of new polymorphs can therefore be beneficial if occurring during development of a product, if stable polymorphs with desirable properties are discovered, or catastrophic, if occurring during manufacturing. Methods to predict the tendency of a compound to display polymorphic behaviour early on in development, as well as the number of polymorphs that can be synthesised, and their structures, would be of profound importance to industrial specialists and material scientists alike.

With developments in recent decades, CSP for organic molecules has seen increasing adoption among industrial sectors such as pharmaceuticals and agrochemicals. Many compounds of industrial relevance are now within the scope of current methods, but the complexity of the calculations involved requires that a careful balance must be struck between computational cost and accuracy. Due to this restriction, issues still arise surrounding the accuracy of the results obtained from common CSP methodologies. This is primarily dependent on the quality of the lattice energy model used to determine relative polymorph stability. If the field of CSP is to see continued growth, further advances in the accuracy of cost efficient approaches are needed.

In this thesis, I will analyse a class of lattice energy models commonly used within several well-established CSP methodologies. Such models are represented by a force field consisting of a hybrid of ab initio derived quantities and data-driven empirical models. A leading source of error in these models stems from poor or inconsistent parameterisation of the empirical component. To address this, I will present a general methodology for the estimation of empirical parameters for this class of models. The methodology uses gradient-based optimisation techniques to tackle large-scale problems, and introduces novel approaches to ensure the reliability and efficiency of the parameter estimation procedure.

To make the parameter estimation approach feasible, this work has led to the construction of a novel code known as Crystal Structure Optimizer -- Rigid Molecules (CSO-RM). The lattice energy model in CSO-RM is formulated over the variables defining the geometry of a rigid-body system. Lattice minimisations of intermolecular energy are performed by optimisation over the rigid-body variables with fixed molecular conformation. The code also calculates various derivatives of intermolecular energy that are used within the parameter estimation algorithm. The implementation of CSO-RM is shown to be remarkably efficient and it supports calculations using both point-charge based and multipole based electrostatic models. The integration of this code within a newly developed parameter estimation algorithm (known as CrystalEstimator) leads to a reduction in computational cost of between 3--4 orders of magnitude compared to contemporary methodologies, while ensuring a high level of confidence in the parameter estimates produced.

Using this methodology, parameter estimates are developed to accurately model interactions between organic molecules containing C, H, O, N, F, Cl, and S atoms. High-quality reference datasets derived from Density Functional Theory (DFT) calculations, also developed in this work, are used to fit the parameter estimates. The resulting parameters sets are compared to commonly-used literature potentials and significant improvements in energy and geometry predictions are observed in line with DFT calculations. In total, 30 sets of parameter estimates are produced consistent with different models for the electrostatic potential. I perform rigorous analysis of the impacts of various modelling choices and make recommendations for model selection. Some of the main deficiencies of current lattice energy models models are also highlighted, prompting directions for future work in this area. Finally, the parameter estimates are validated in CSP studies of several rigid compounds. In each case, the results obtained are comparable or better using the parameter estimates obtained in this work than another leading parameterisation.