The phase-seeding method for solving non-centrosymmetric crystal structures: a challenge for artificial intelligence.

Abstract

The overall crystallographic process involves acquiring experimental data and using crystallographic software to find the structure solution. Unfortunately, while diffracted intensities can be measured, the corresponding phases - needed to determine atomic positions - remain experimentally inaccessible (phase problem). Direct methods and the Patterson approach have been successful in solving crystal structures but face limitations with large structures or low-resolution data. Current artificial intelligence (AI) based approaches, such as those recently developed by Larsen et al. [Science (2024), 385, 522-528], have been applied with success to solve centrosymmetric structures, where the phase is binary (0 or π). The current work proposes a new phasing method designed for AI integration, applicable also to non-centrosymmetric structures, where the phase is a continuous variable. The approach involves discretizing the initial phase values for non-centrosymmetric structures into a few distinct values (e.g. values corresponding to the four quadrants). This reduces the complex phase problem from a continuous regression task to a multi-class classification problem, where only a few phase seed values need to be determined. This discretization allows the use of a smaller training dataset for deep learning models, reducing computational complexity. Our feasibility study results show that this method can effectively solve small, medium and large structures, with the minimum percentage of phase seeds (three or four points in the interval [0, 2π]), and 10% to 30% of seed symmetry-independent reflections. This phase-seeding method has the potential to extend AI-based approaches to solve crystal structures ab initio, regardless of complexity or symmetry, by combining AI classification algorithms with classical phasing procedures.