# Hyperspatial optimisation of structures

## TL;DR

This paper introduces a hyperspatial optimization method that enhances the efficiency of structure prediction by avoiding local minima traps, significantly accelerating the search process especially for complex systems.

## Contribution

The authors demonstrate that starting optimizations in higher-dimensional hyperspaces reduces trapping in local minima, improving the speed of structure prediction by up to two orders of magnitude.

## Key findings

- Random structure search is significantly accelerated in hyperspace.
- Performance improvements are most notable for difficult systems.
- The method benefits all local optimization-based structure prediction approaches.

## Abstract

Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy landscape. In many cases these local minima are relatively high in energy, and inspection reveals that they are trapped, tangled, or otherwise frustrated in their descent to a lower energy configuration. Strategies have been developed which attempt to overcome these traps, such as classical and quantum annealing, basin/minima hopping, evolutionary algorithms and swarm based methods. Random structure search makes no attempt to avoid the local minima, and benefits from a broad and uncorrelated sampling of configuration space. It has been particularly successful in the first principles prediction of unexpected new phases of dense matter. Here it is demonstrated that by starting the structural optimisations in a higher dimensional space, or hyperspace, many of the traps can be avoided, and that the probability of reaching low energy configurations is much enhanced. Excursions into the extra dimensions are progressively eliminated through the application of a growing energetic penalty. This approach is tested on hard cases for random search - clusters, compounds, and covalently bonded networks. The improvements observed are most dramatic for the most difficult ones. Random structure search is shown to be typically accelerated by two orders of magnitude, and more for particularly challenging systems. This increase in performance is expected to benefit all approaches to structure prediction that rely on the local optimisation of stochastically generated structures.