Bias caused by a popular weighting scheme

Area of Science:

• Crystallography
• Materials Science
• Computational Chemistry

Background:

• The SHELXL refinement program is widely used in X-ray crystallography for determining crystal structures.
• Weighting schemes in crystallographic refinement are crucial for accurate structure determination.
• Underestimation of standard uncertainties (s.u.) in observed intensities is a common issue.

Purpose of the Study:

• To investigate the impact of underestimated standard uncertainties on residuals within SHELXL-like weighting schemes.
• To quantify the bias introduced by such underestimations in crystallographic data.
• To assess the effect on key refinement parameters, such as equivalent displacement parameters (U_equiv).

Main Methods:

• Simulations were performed to model the effects of underestimated intensity standard uncertainties.
• The study focused on the residuals generated by a SHELXL-like weighting scheme.
• The symmetry of residuals and the average increase in U_equiv were analyzed.

Main Results:

• Underestimating standard uncertainty values by a factor of 5 significantly biases residuals.
• This underestimation destroys the symmetry of residuals around zero.
• Simulations showed an average increase of 3.35% in equivalent displacement parameters (U_equiv).

Conclusions:

• The common practice of underestimating standard uncertainties in intensity data introduces significant bias in crystallographic refinements using SHELXL-like methods.
• This bias can lead to inaccurate structural parameters, specifically affecting atomic displacement parameters.
• Careful assessment and accurate estimation of standard uncertainties are critical for reliable crystal structure analysis.