A weighting scheme for least-squares structure refinement

Carruthers, Janet; Watkin, David J.

doi:10.1107/s0567739479001613

Cited by 508 publications

(270 citation statements)

References 2 publications

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“…The high values found for the isotropic temperature factors of the F atoms of the hexafluorophosphate groups suggested some disorder and slack constraints (Waser, 1963;Rollett, 1969) were applied. In the final stages of the refinement an overall isotropic extinction parameter was introduced (Larson, 1967) and a Chebyshev weighting scheme was used (Carruthers & Watkin, 1979a).…”

Section: Methodsmentioning

confidence: 99%

The structures of mono- and bis-arene tungsten derivatives: (I) bis(η6-toluene)tungsten, (II) hydridobis(η6-toluene)tungsten hexafluorophosphate, (III) hydridobis(η6-monofluorobenzene)tungsten hexafluorophosphate, (IV) dichlorohydrido(η6-toluene)bis(trimethylphosphine)tungsten hexafluorophosphate, (V) bis(acetonitrile)(η3-allyl)(η6-toluene)tungsten hexafluorophosphate

Prout¹,

Gourdon²,

Couldwell³

et al. 1982

Acta Crystallogr Sect B

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Section: Methodsmentioning

confidence: 99%

The structures of mono- and bis-arene tungsten derivatives: (I) bis(η6-toluene)tungsten, (II) hydridobis(η6-toluene)tungsten hexafluorophosphate, (III) hydridobis(η6-monofluorobenzene)tungsten hexafluorophosphate, (IV) dichlorohydrido(η6-toluene)bis(trimethylphosphine)tungsten hexafluorophosphate, (V) bis(acetonitrile)(η3-allyl)(η6-toluene)tungsten hexafluorophosphate

Prout¹,

Gourdon²,

Couldwell³

et al. 1982

Acta Crystallogr Sect B

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“…The final values of R and R w were (I) 0.041, 0.057; (II) 0.042, 0.057; (III) 0.071, 0.064 and (IV) 0.042, 0.052. In each case a Chebyshev weighting scheme (Carruthers & Watkin, 1979) (21) 517 (49) 11286 (64) 1702 (14) 467 (46) H (22) 845 (54) 10864 (60) 704 (14) 467 (46) H (23) 2145 (58) 12949 (34) 1148 (19) 467 (46) * In Tables 1, 2, 3 and 4, for the non-hydrogen atoms, Ueq --(UIU2Ua) , where UI, U2 and U 3 are the mean square displacements (A 2) along each of the principal axes of the thermal ellipsoid. Results and discussion …”

Section: Additional Crystal Data and Data-collection Parametersmentioning

confidence: 99%

Structures of the nitrosamides: (I) N-methyl-N-nitrosourea, (II) N,N'-dimethyl-N-nitrosourea, (III) 2-nitroso-2-azabicyclo[2.2.2]octan-3-one and (IV) N-methyl-N-nitroso-p-nitrobenzamide

Prout¹,

Fail²,

Hernández-Cassou³

et al. 1982

Acta Crystallogr Sect B

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“…Particularly interesting is the robust weighting scheme adopted by Carruthers & Watkin (1979) implemented in the crystallographic least-squares code CRYSTALS (Betteridge et al, 2003). This weight is a function of the discrepancy between the observed reflection and the calculated one.…”

Section: Robust Weights In a Crystal Structure Refinementmentioning

confidence: 99%

Iteratively reweighted least squares in crystal structure refinements

Merli

Sciascia

2011

Acta Cryst Sect A

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The use of robust techniques in crystal structure multipole refinements of small molecules as an alternative to the commonly adopted weighted least squares is presented and discussed. As is well known, the main disadvantage of leastsquares fitting is its sensitivity to outliers. The elimination from the data set of the most aberrant reflections (due to both experimental errors and incompleteness of the model) is an effective practice that could yield satisfactory results, but it is often complicated in the presence of a great number of bad data points, whose one-by-one elimination could become unattainable. This problem can be circumvented by means of a robust least-squares regression that minimizes the influence of outliers. This work is aimed at showing the capability of a robust regression to achieve an higher reliability of the least-squares estimates with respect to the traditional weighted least-squares crystal structure refinement in terms of both accuracy and precision. The results can be considered encouraging and represent a starting point for future developments.

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A weighting scheme for least-squares structure refinement

Cited by 508 publications

References 2 publications

Structures of the nitrosamides: (I) N-methyl-N-nitrosourea, (II) N,N'-dimethyl-N-nitrosourea, (III) 2-nitroso-2-azabicyclo[2.2.2]octan-3-one and (IV) N-methyl-N-nitroso-p-nitrobenzamide

Iteratively reweighted least squares in crystal structure refinements

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