X‐ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review

• Published in: Acta crystallographica Section B, Structural science, crystal engineering and materials Structural science, crystal engineering and materials, 2022-06, Vol.78 (3-1), p.312-332
• Main Authors: Davidson, Max L., Grabowsky, Simon, Jayatilaka, Dylan
• Format: Article
• Language: English
• Subjects: Crystallography, X-Ray; halting problem; Hirshfeld atom; Probability distribution; Radiography; Wave functions; X-Ray Diffraction; X-Rays; X‐ray constrained wavefunction; X‐ray wavefunction refinement
• ISSN: 2052-5206; 2052-5192; 2052-5206
• DOI: 10.1107/S2052520622004097

The X‐ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X‐ray diffraction data is reviewed. The two‐center probability distribution model used to perform nuclear‐position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87–100] is carefully distinguished from the newer one‐center probability distribution model. In the one‐center model, Hirshfeld atoms are used, and the Hirshfeld atom based X‐ray constrained wavefunction (HA‐XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X‐ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method – the procedure by which one determines when overfitting has occurred – is named and work on it reviewed. Methods for reconstructing `experimental model wavefunctions' from X‐ray data are reviewed and clarified, and the key problem of deciding when to terminate the wavefunction reconstruction procedure is defined as 'the halting problem'. The role of Hans‐Beat Bürgi in all of this is described.