Solving Crystal Structures by Carrying Out the Calculation of the Single-Atom R1 Method in a Lottery Mode

TL;DR

This paper introduces a lottery-based scheme for the single-atom R1 method in crystal structure determination, enabling automated, stochastic improvement of models without user intervention, leading to successful structure solutions.

Contribution

The paper presents a novel lottery scheme that automates and enhances the sR1 method by utilizing random splitting and statistical fluctuations to improve structure solutions.

Findings

The lottery scheme effectively guides the sR1 method towards correct structures.

Statistical fluctuations enable the selection of better models over cycles.

The approach reduces the need for user intervention in structure determination.

Abstract

As originally designed [Zhang & Donahue (2024), Acta Cryst. A80, 2370248.], after one cycle of calculation, the single-atom R1 (sR1) method required a user to intelligently determine a partial structure to start the next cycle. In this paper, a lottery scheme has been designed to randomly split a parent model into two child models. This allows the calculation to be carried out in care-free manner. By chance, one child model may have higher amounts of "good" atoms than the parent model. Thus, its expansion in the next cycle favors an improved model. These "lucky" results are carried onto the next cycles. while "unlucky" results in which no improvements occur are discarded. Furthermore, unchanged models are carried onto the next cycles in those "unlucky" occasions. On average a child model has the same fraction of "good" atoms as the parent. Only a substantial statistical fluctuation results in appreciable deviation. This lottery scheme works because such fluctuations do happen. Indeed, test applications with the computing power accessibly by the author have demonstrated that the designed scheme can drive an sR1 calculation to or close to reaching a correct structure solution.