Two metrics for quantifying systematic errors in diffraction experiments: systematic errors in the variance of the...

Area of Science:

• Crystallography
• Materials Science
• Data Analysis

Background:

• Single-crystal X-ray and neutron diffraction are crucial for determining molecular structures.
• Systematic errors can compromise the accuracy of structural models and data quality.
• The weighted agreement factor (wR) is a key metric for assessing data quality.

Purpose of the Study:

• To quantify the impact of systematic errors on the weighted agreement factor in diffraction experiments.
• To investigate the prevalence and causes of increased agreement factors in published data sets.
• To highlight the critical role of accurate standard uncertainties (s.u.) in data evaluation.

Main Methods:

• Analysis of 314 published crystal diffraction data sets.
• Quantification of the increase in the weighted agreement factor due to systematic errors.
• Comparison of observed agreement factors with the theoretical minimum for each data set.

Main Results:

• Systematic errors increased the weighted agreement factor by a factor of g = 3.31 (or more) in 50% of small-molecule data sets.
• Common systematic errors include twinning, disorder, and neglect of bonding densities.
• Inadequate s.u.(I_obs) were identified as a significant, common systematic error.

Conclusions:

• The accuracy of standard uncertainties (s.u.) is paramount for reliable data quality assessment in crystallography.
• Insufficiently accurate s.u.(I_obs) pose a threat not only to model parameters but to the entire evaluation procedure.
• A large increase in the weighted agreement factor serves as a warning sign for both known and unknown systematic errors, including poor s.u. estimations.