Powder-Diffraction-Based Structural Comparison for Crystal Structure Prediction without Prior Indexing

29 March 2024, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


The objective of crystal structure prediction (CSP) is to predict computationally the thermodynamically stable crystal structure of a compound from its stoichiometry or its molecular diagram. Crystal similarity indices measure the degree of similarity between two crystal structures, and are essential in CSP because they are used to identify duplicates. In addition, powder-based indices, which are based on comparing X-ray diffraction patterns, also allow the use of experimental X-ray powder diffraction data to inform the CSP search. Powder-assisted CSP presents two unique difficulties: i) the experimental and computational structures are not entirely comparable because the former is subject to thermal expansion from lattice vibrations, and ii) experimental patterns present features (noise, background contribution, varying peak shapes, etc.) that are not easily predictable computationally. In this work, we present a powder-based similarity index (GPWDF) based on a modification of de Gelder et al.'s index using cross-correlation functions that can be calculated analytically. Based on GPWDF, we also propose a variable-cell similarity index (VC-GPWDF) that assigns a high similarity score to structures that differ only by a lattice deformation and takes advantage of the analytical derivatives of GPWDF with respect to the lattice parameters. VC-GPWDF can be used to identify similarity between: two computational structures generated using different methods, a computational and a experimental structure, and two experimental structures measured under different conditions (e.g. different temperature and pressure). In addition, VC-GPWDF can also be used to compare crystal structures with experimental patterns in combination with an automatic pre-processing step. The proposed similarity indices are simple, efficient, and fully automatic. They require no indexing of the experimental pattern or a guess of the space group, account for deformations caused by varying experimental conditions, give meaningful results even when the experimental pattern is of very poor quality, and have a cost does not increase with the flexibility of the molecular motif.


Crystal structure prediction
Molecular crystals
Crystal structure comparison
X-ray powder diffraction

Supplementary materials

Supporting Information: Powder-Diffraction-Based Structural Comparison for Crystal Structure Prediction without Prior Indexing
Application of the proposed method to the experimental patterns in the work of Mayo et al. (Chem. Sci. 14 (2023) 4777–4785).


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.