Powder-diffraction-based structural comparison for crystal structure prediction without prior indexing

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. Powder-based indices, which are based on comparing X-ray diffraction patterns, 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. This work presents a powder-based similarity index (GPWDF) based on a modification of the index introduced by de Gelder, Wehrens & Hageman [J. Comput. Chem. (2001), 22, 273–289] using cross-correlation functions that can be calculated analytically. Based on GPWDF, a variable-cell similarity index (VC-GPWDF) is also proposed that assigns a high similarity score to structures that differ only by a lattice deformation and which 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, between a computational and an experimental structure, and between two experimental structures measured under different conditions (e.g. different temperature and pressure). 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 do not require indexing of the experimental pattern or a guess of the space group, they account for deformations caused by varying experimental conditions, they give meaningful results even when the experimental pattern is of very poor quality, and their computational cost does not increase with the flexibility of the molecular motif.