The influence of refinement strategies on the wavefunctions derived from an experiment

Abstract

The synergy between theory and experiment found in X-ray wavefunction refinement (XWR) makes it one of the most compelling techniques available for chemical physics. The foremost benefit of XWR – obtaining wavefunctions constrained to experimental data – is at the same time its Achilles heel, because of the dependence of the results on the quality of both empirical and theoretical data. The purpose of this work is to answer the following: What is the effect of the refinement strategy and manipulation of input data on the physical properties obtained from XWR? With that in mind, cutoffs based on data resolution and F/σ(F) ratios were applied for both steps of XWR, the Hirshfeld atom refinement (HAR) and the X-ray constrained wavefunction fitting (XCW), for four selected systems: sulfur dioxide, urea, carbamazepine and oxalic acid. The effects of changing the weighting scheme or the method to transform σ(F 2) to σ(F) were also analysed. The results show that while HAR always reaches the same result, XCW is extremely sensitive to crystallographic data manipulation. This is a result of the variability of the experimental uncertainties for different resolution shells, and of not having proper standard uncertainties. Therefore, the use of distinct constraints for each resolution interval in XCW is proposed to fix this instability.

X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate

“…This idea is quite similar to the one used in the protein R free method (Bru ¨nger, 1992). It is also similar to suggestions by Sanjuan-Szklarz et al (2020) and Landeros-Rivera et al (2021), to break data sets into low and high resolution parts. These approaches are not investigated further in this paper but may be of use in the future.…”

“…That project was never completed in a satisfactory way (Dacombe, 2013). The present work, all previous investigations of the halting problem, and the work of Landeros-Rivera et al (2021) represent contributions to that project.…”

“…For this system, and for electron density features, this means that fitting to the best possible GoF 2 before convergence ceases as normally done is justified. However, for other features such as bond critical points which are more sensitive to the model (Landeros-Rivera et al, 2021) or in cases where it is known that overfitting occurs this may not be the case so that the halting protocols introduced here could be reinvestigated.…”

“…There has recently been much interest in the technique of X-ray constrained (or restrained) wavefunction (XCW) fitting (Jayatilaka, 1998;), but doubts have been raised about the accuracy, reproducibility and the meaning of the electron densities obtained from such experimental wavefunctions (Landeros-Rivera et al, 2021;Kleemiss et al, 2021;Grabowsky et al, 2020;Ernst et al, 2020;Genoni et al, 2017). To address these concerns, and in preparation for this paper, we have therefore first reviewed the status of the XCW method, in Davidson et al (2022).…”

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

“…The XCW method has recently received renewed interest (Landeros-Rivera et al, 2021;Macetti et al, 2021;Grabowsky et al, 2020;Ernst et al, 2020;, especially since the development of the Hirshfeld atom refinement (HAR) method (Jayatilaka & Dittrich, 2008;Capelli et al, 2014;Woin ´ska et al, 2016). This is because HAR, also a development in the QCr field, better-known than the XCW method, is capable of obtaining hydrogen atom positions and ADPs in agreement with independent neutron diffraction experiments in a 'fairly automatic and standard way' (Woin ´ska et al, 2016).…”