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A Bayesian approach to NMR crystal structure determination.

Edgar A Engel1, Andrea Anelli, Albert Hofstetter

  • 1Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. michele.ceriotti@epfl.ch.

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Summary

This study introduces a Bayesian framework to quantify confidence in crystal structure determination using Nuclear Magnetic Resonance (NMR) spectroscopy. It improves accuracy by reassessing errors in chemical shift predictions, enhancing NMR crystallography reliability.

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Area of Science:

  • Solid-state Nuclear Magnetic Resonance (NMR) spectroscopy.
  • Crystallography.
  • Computational chemistry.

Background:

  • NMR spectroscopy is crucial for determining molecular and material structures in powdered forms.
  • Structure determination relies on matching experimental NMR chemical shifts with candidate structures.
  • Current methods using electronic-structure calculations or machine learning face reliability issues due to prediction errors.

Purpose of the Study:

  • To develop a Bayesian framework for quantifying confidence in experimental crystal structure identification using NMR chemical shifts.
  • To reassess and improve the accuracy of chemical shift predictions and their associated uncertainties.
  • To enhance the reliability and efficiency of NMR crystallography.

Main Methods:

  • Proposed a Bayesian framework to assess confidence in structure determination based on known errors in electronic-structure methods.
  • Applied the framework to six organic molecular crystals.
  • Introduced a visualization tool to assess similarity between candidate structures and their chemical shifts.
  • Extended the ShiftML model for improved efficiency, accuracy, and uncertainty evaluation.

Main Results:

  • Demonstrated the Bayesian framework's effectiveness in determining confidence levels for crystal structures.
  • Showed that commonly used error values for calculated 13C shifts are underestimated.
  • Established that more accurate, self-consistent uncertainties improve structure determination accuracy using 13C shifts.
  • Validated the enhanced ShiftML model as an efficient and accurate alternative to first-principles calculations in NMR crystallography.

Conclusions:

  • The proposed Bayesian framework provides a reliable method for quantifying confidence in NMR-based structure determination.
  • Accurate assessment of uncertainties in chemical shift predictions is critical for improving NMR crystallography.
  • The enhanced ShiftML model offers a robust and efficient approach for NMR crystallography, comparable to traditional methods.