An alternative to the goodness of fit

Henn, Julian

doi:10.1107/s2053273316013206

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…where ( 2 ) is the standard deviation of 2 , which is computed as ð2=N R Þ 1=2 . It was proposed that |n 1 | > 3 can be used as a criterion for a significant difference of 2 from 1 (Henn, 2016). When applied to the same HAR of SO 2 a value of n 1 = 107.8 is obtained, confirming that the (F) are not optimal.…”

Section: Summary and Discussionmentioning

confidence: 99%

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

Landeros‐Rivera¹,

Contreras‐García²,

Dominiak³

2021

Acta Crystallogr B Struct Sci Cryst Eng Mater

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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.

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Section: Summary and Discussionmentioning

confidence: 99%

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

Landeros‐Rivera¹,

Contreras‐García²,

Dominiak³

2021

Acta Crystallogr B Struct Sci Cryst Eng Mater

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“…A particularly helpful metric for the detection of too-large standard deviations is the alternative goodness of fit (aGoF), as this might become smaller than one in this case, whereas the GoF may still remain larger than one (Henn, 2019(Henn, , 2016. To give a very brief explanation for these findings: The deviation of the GoF is based on the 2 distribution that describes independent identically distributed random numbers.…”

Section: Normal Probability Plotsmentioning

confidence: 99%

Progress in detection of and correction for low-energy contamination

Domagala,

Nourd,

Diederichs

et al. 2023

J Appl Cryst

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Contamination with low-energy radiation leads to an increased number of weighted residuals being larger in absolute terms than three standard uncertainties. For a Gaussian distribution, these rare events occur only in 0.27% of all cases, which is a small number for small- to medium-sized data sets. The correct detection of rare events – and an adequate correction procedure – thus relies crucially on correct standard uncertainties, which are often not available [Henn (2019), Crystallogr. Rev. 25, 83–156]. It is therefore advisable to use additional, more robust, metrics to complement the established ones. These metrics are developed here and applied to reference data sets from two different publications about low-energy contamination. Other systematic errors were found in the reference data sets. These errors compromise the correction procedures and may lead to under- or overcompensation. This can be demonstrated clearly with the new metrics. Empirical correction procedures generally may be compromised or bound to fail in the presence of other systematic errors. The following systematic errors, which were found in the reference data sets, need to be corrected for prior to application of the low-energy contamination correction procedure: signals of 2λ contamination, extinction, disorder, twinning, and too-large or too-low standard uncertainties (this list may not be complete). All five reference data sets of one publication show a common resolution-dependent systematic error of unknown origin. How this affects the correction procedure can be stated only after elimination of this error. The methodological improvements are verified with data published by other authors.

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“…They concluded that two common sources of systematic errors in charge-density studies are data processing errors and the underestimation of large values (Henn & Meindl, 2015b). Recently they state that in most charge-density studies there is a correlation between the squared residuals and the variance of the experimental standard uncertainties leading to meaningless GOF values (Henn, 2016).…”

Section: Residual Values and Detection Of Systematic Errorsmentioning

confidence: 99%

Experimental charge-density studies: data reduction and model quality: the more the better?

Herbst‐Irmer

2017

Acta Crystallogr Sect B

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In this review, recent developments concerning data and model quality in experimental charge-density investigations from a personal view-point are described. Data quality is not only achieved by the high resolution, high I/σ(I) values, low merging R values and high multiplicity. The quality of the innermost reflections especially is crucial for mapping the density distribution of the outermost valence electrons and can be monitored by (I/σ). New detector technologies seem to be promising improvements. Empirical corrections to correct for low-energy contamination of mirror-focused X-ray data and for resolution- and temperature-dependent errors caused by factors such as thermal diffuse scattering are described. Shashlik-like residual density patterns can indicate the need for an anharmonic description of the thermal motion of individual atoms. The physical reliability of the derived model must be thoroughly analysed. The derived probability density functions for the mean-squared atomic vibrational displacements especially should have only small negative values. The treatment of H atoms has been improved by methods to estimate anisotropic thermal motion. For very high resolution data, the polarization of the core density cannot be neglected. Several tools to detect systematic errors are described. A validation tool is presented that easily detects when the refinement of additional parameters yields a real improvement in the model or simply overfits the given data. In all investigated structures, it is proved that the multipole parameters of atoms with a comparable chemical environment should be constrained to be identical. The use of restraints could be a promising alternative.

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An alternative to the goodness of fit

Cited by 7 publications

References 27 publications

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

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

Progress in detection of and correction for low-energy contamination

Experimental charge-density studies: data reduction and model quality: the more the better?

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