Global Optimization of Atomic Structures in Extra Dimensions

Global optimization of atomic structures comprise a set of methods intended to find the lowest energy configuration for a given set of atoms in as few steps as possible. Traditionally these methods consist of different ways of sampling and navigating a potential energy surface, as calculated by electronic structure methods like density functional theory (DFT). Recently machine learning methods trained on databases of e.g. DFT calculations have become increasingly successful at replacing the electronic structure calculations without loss of accuracy, but at a fraction of the computational cost. Such approaches accelerate global optimization methods but remain fundamentally limited to the efficiency achievable on the actual potential energy surface. In this thesis, we go beyond the limitations of DFT by formulating an atomic descriptor extending the atoms with additional nonphysical degrees of freedom. These include chemical identity coordinates, atomic existence and hyperspatial coordinates all of which can be energetically minimized separately or simultaneously. The minimization is performed on a surrogate potential energy surface generated by Gaussian process regression trained on DFT calculations as part of a Bayesian optimization algorithm, where it is assured that all relaxational end states and training points are physically valid.
The method is shown to successfully interpolate energy and force predictions from a training set of physically valid structures to structures with nonphysical coordinates. The inclusion of extra degrees of freedom significantly improves the efficiency of optimization of both clusters and bulk materials by circumventing energy barriers encountered in the conventional potential energy surface. The chemical identity and hyperspatial coordinates provide by far the largest benefit, with simultaneous optimization of the two being especially effective. The inclusion of atomic existence provide only minor improvement, but appear to work better when combined with simultaneous optimization of chemical identities.
Chemical identity coordinates and atomic existence are shown to spontaneously converge towards integer values representing real chemical elements as opposed to the hyperspatial coordinates from which atoms have to be squeezed back into the physical space by a penalizing potential.
The final part of the thesis demonstrates how universal machine learning potentials (MLPs) can be used as a prior for an actively learning Gaussian process model. The inclusion of MLPs improves global optimization success rates, while the Gaussian process captures additional information not provided by the MLP.