A method to estimate statistical errors of properties derived from charge-density modelling.

Bertrand Fournier,Benoît Guillot,Christian Jelsch,Claude Lecomte,Eduardo C Escudero-Adán

doi:10.1107/s2053273318004308

Abstract

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance-covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.

Highlights

Errors on electron-density-derived properties, such as topological characteristics or electrostatic potential, are generally poorly addressed in the relevant literature
In the XD2006 program (Volkov et al, 2006), there is a feature that allows one to compute estimated uncertainties of the electron density (r), of the Laplacian r2 and of dipole moment values using the variance–covariance matrix, but it only accounts for the contributions of some of the parameters used in the Hansen & Coppens (1978) model, i.e. monopole and multipole populations
The current study addresses the uncertainty on properties related to the precision of measurements

Summary

Introduction

Errors on electron-density-derived properties, such as topological characteristics or electrostatic potential, are generally poorly addressed in the relevant literature. In the XD2006 program (Volkov et al, 2006), there is a feature that allows one to compute estimated uncertainties of the electron density (r), of the Laplacian r2 and of dipole moment values using the variance–covariance matrix, but it only accounts for the contributions of some of the parameters used in the Hansen & Coppens (1978) model, i.e. monopole and multipole populations. It implies that the propagation of errors due to the contributions of the atomic coordinates and of the contraction/expansion coefficients and 0 is not taken into account. When several experimental X-ray diffraction data sets collected during distinct and independent measurements are available for the same compound, it becomes possible to study the reproducibility of

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Conclusion