Validation of experimental charge-density refinement strategies: when do we overfit?

Area of Science:

• Crystallography
• Computational Chemistry
• Data Analysis

Background:

• Multipole refinement is crucial for accurate modeling of electron density in crystals.
• Distinguishing between model improvement and overfitting in refinement procedures can be challenging.

Purpose of the Study:

• To develop and validate a cross-validation method for assessing multipole refinement strategies.
• To establish criteria for parameter constraints in multipole refinement.
• To enhance error diagnostics in crystallographic data analysis.

Main Methods:

• A cross-validation approach was applied to evaluate different multipole refinement strategies.
• The method was tested on various datasets to assess its effectiveness.
• Parameter distributions from multiple refinements were analyzed for error detection.

Main Results:

• The cross-validation method effectively distinguishes between model improvement and overfitting.
• It was demonstrated that multipole parameters for atoms in comparable chemical environments should be constrained to be identical.
• Automated analysis provided parameter distributions useful for error diagnostics, identifying issues like incorrect reflections or parameter definitions.

Conclusions:

• The proposed cross-validation method is a reliable tool for optimizing multipole refinement.
• Constraining equivalent atomic parameters improves model accuracy and prevents overfitting.
• The method offers advanced diagnostics for crystallographic data quality and parameter reliability.