Why direct and post-refinement determinations of absolute structure may give different results.

Direct determination of the Flack parameter as part of the structure refinement procedure usually gives different, though similar, values to post-refinement methods. The source of this discrepancy has been probed by analysing a range of data sets taken from the recent literature. Most significantly, it was observed that the directly refined Flack (x) parameter and its standard uncertainty are usually not much influenced by changes in the refinement weighting schemes, but if they are then there are probably problems with the data or model. Post-refinement analyses give Flack parameters strongly influenced by the choice of weights. Weights derived from those used in the main least squares lead to post-refinement estimates of the Flack parameters and their standard uncertainties very similar to those obtained by direct refinement. Weights derived from the variances of the observed structure amplitudes are more appropriate and often yield post-refinement Flack parameters similar to those from direct refinement, but always with lower standard uncertainties. Substantial disagreement between direct and post-refinement determinations are strongly indicative of problems with the data, which may be difficult to identify. Examples drawn from 28 structure determinations are provided showing a range of different underlying problems. It seems likely that post-refinement methods taking into account the slope of the normal probability plot are currently the most robust estimators of absolute structure and should be reported along with the directly refined values.

[1]  S. Parsons,et al.  Analysing Friedel averages and differences. , 2012, Acta crystallographica. Section A, Foundations of crystallography.

[2]  D. I. Stuart,et al.  An empirical method for correcting diffractometer data for absorption effects , 1983 .

[3]  R. Baggio,et al.  μ-Acetato-μ-aqua-μ-hydroxido-bis[(1,10-phenanthroline)copper(II)] dinitrate monohydrate. , 2011, Acta crystallographica. Section C, Crystal structure communications.

[4]  M. Merli,et al.  Iteratively reweighted least squares in crystal structure refinements. , 2011, Acta crystallographica. Section A, Foundations of crystallography.

[5]  H. Flack.  Absolute-structure reports. , 2013, Acta crystallographica. Section C, Crystal structure communications.

[6]  S. Parsons,et al.  Use of intensity quotients and differences in absolute structure refinement , 2013, Acta crystallographica Section B, Structural science, crystal engineering and materials.

[7]  G. Bernardinelli,et al.  Applications and properties of the Bijvoet intensity ratio. , 2008, Acta crystallographica. Section A, Foundations of crystallography.

[8]  G. Sheldrick.  SHELXT – Integrated space-group and crystal-structure determination , 2015, Acta crystallographica. Section A, Foundations and advances.

[9]  Richard I. Cooper,et al.  The derivation of non-merohedral twin laws during refinement by analysis of poorly fitting intensity data and the refinement of non-merohedrally twinned crystal structures in the program CRYSTALS , 2002 .

[10]  Rob W. W. Hooft,et al.  Determination of absolute structure using Bayesian statistics on Bijvoet differences , 2008, Journal of applied crystallography.

[11]  D. Rabinovich,et al.  Absolute configuration determination by anomalous scattering of light atoms. Have the limits been reached , 1980 .

[12]  M. Sadki,et al.  Practical applications of averages and differences of Friedel opposites. , 2011, Acta crystallographica. Section A, Foundations of crystallography.

[13]  Kay Diederichs.  Quantifying instrument errors in macromolecular X-ray data sets. , 2010, Acta crystallographica. Section D, Biological crystallography.

[14]  A. Oliver,et al.  Disorder and conformational analysis of methyl β-D-galactopyranosyl-(1→4)-β-D-xylopyranoside. , 2012, Acta crystallographica. Section C, Crystal structure communications.

[15]  J. S. Reid,et al.  The Analytical Calculation of Absorption in Multifaceted Crystals , 1995 .

[16]  P. Ballester,et al.  The use of Mo Kα radiation in the assignment of the absolute configuration of light-atom molecules; the importance of high-resolution data. , 2014, Acta crystallographica Section B, Structural science, crystal engineering and materials.

[17]  H. Flack,et al.  On enantiomorph‐polarity estimation , 1983 .

[18]  D. Langs,et al.  Data averaging with normal down-weighting of outliers , 1987 .

[19]  H. J. Milledge,et al.  Computing Methods and the Phase Problem in X-ray Crystal Analysis , 1962 .

[20]  Manfred S. Weiss,et al.  Global indicators of X-ray data quality , 2001 .

[21]  M. Dušek,et al.  Mixed crystals of 2-carbamoylguanidinium with hydrogen fluorophosphonate and hydrogen phosphite in the ratios 1:0, 0.76 (2):0.24 (2) and 0.115 (7):0.885 (7). , 2012, Acta crystallographica. Section C, Crystal structure communications.

[22]  W. Parrish.  Results of the IUCr precision lattice‐parameter project , 1960 .

[23]  Michael B. Hursthouse,et al.  Experimental and theoretical study of the charge density in 2‐methyl‐4‐nitroaniline , 1992 .

[24]  D. Cruickshank,et al.  Parameter errors in polar space groups caused by neglect of anomalous scattering , 1967 .

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[26]  P. Evans,et al.  Scaling and assessment of data quality. , 2006, Acta crystallographica. Section D, Biological crystallography.

[27]  H. Xiong,et al.  A 2'-deoxycytidine long-linker click adduct forming two conformers in the asymmetric unit. , 2012, Acta crystallographica. Section C, Crystal structure communications.

[28]  D. Rogers,et al.  On the application of Hamilton's ratio test to the assignment of absolute configuration and an alternative test , 1981 .

[29]  A. Spek,et al.  Using the t‐distribution to improve the absolute structure assignment with likelihood calculations , 2010 .

[30]  S. Ealick,et al.  The molecular structures and absolute configurations of eupalmerin acetate and eupalmerin acetate dibromide at low temperature , 1975 .

[31]  A. L. Thompson,et al.  CRYSTALS enhancements: absolute structure determination , 2011 .

[32]  A. Spek,et al.  Centrosymmetric and pseudo-centrosymmetric structures refined as non-centrosymmetric. , 2006, Acta crystallographica. Section B, Structural science.

[33]  P. Wood,et al.  Applications of leverage analysis in structure refinement , 2012 .

[34]  J. Carruthers,et al.  A weighting scheme for least-squares structure refinement , 1979 .

[35]  W. C. Hamilton.  Significance tests on the crystallographic R factor , 1965 .

[36]  P. Pattison,et al.  Probing structural chirality with high-energy synchrotron radiation , 2016 .

[37]  D. Cruickshank,et al.  The comparison of theoretical and experimental determinations of molecular structures, with applications to naphthalene and anthracene , 1953 .

[38]  S. Abrahams,et al.  Normal probability plot analysis of error in measured and derived quantities and standard deviations , 1971 .

[39]  H. Flack,et al.  Absolute structure determination using CRYSTALS. , 2016, Acta crystallographica. Section C, Structural chemistry.