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X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review.

Max L Davidson1, Simon Grabowsky2, Dylan Jayatilaka1

  • 1School of Molecular Sciences, The University of Western Australia, 35 Stirling Highway, Crawley 6009, Western Australia, Australia.

Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials
|June 13, 2022
PubMed
Summary

This study reviews the X-ray constrained wavefunction (XCW) method for experimentally reconstructing wavefunctions. It introduces the novel Hirshfeld atom-based XCW (HA-XCW) procedure and discusses the critical issue of overfitting in X-ray wavefunction refinement.

Keywords:
Hirshfeld atomX-ray constrained wavefunctionX-ray wavefunction refinementhalting problem

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Area of Science:

  • Crystallography
  • Quantum Chemistry
  • Materials Science

Background:

  • The X-ray constrained wavefunction (XCW) procedure enables experimental wavefunction reconstruction from X-ray diffraction data.
  • Distinguishing between two-center and one-center probability distribution models is crucial for accurate wavefunction determination.

Purpose of the Study:

  • To review the established X-ray constrained wavefunction (XCW) procedure.
  • To introduce and describe the novel Hirshfeld atom-based XCW (HA-XCW) procedure and its implementation.
  • To refine the definition of the X-ray wavefunction refinement (XWR) method and address the overfitting problem in XCW.

Main Methods:

  • Review of the two-center probability distribution model for nuclear-position averaging.
  • Description of the one-center probability distribution model utilizing Hirshfeld atoms.
  • Detailed explanation of the efficient implementation of the Hirshfeld atom-based XCW (HA-XCW) procedure.
  • Refinement of the X-ray wavefunction refinement (XWR) method definition.

Main Results:

  • Clear distinction established between the two-center and one-center probability distribution models.
  • The Hirshfeld atom-based XCW (HA-XCW) procedure is presented for the first time with an efficient implementation.
  • The critical issue of overfitting in XCW methods, termed the 'halting problem', is identified and discussed.

Conclusions:

  • The HA-XCW procedure offers an advancement in experimental wavefunction determination.
  • Addressing the overfitting 'halting problem' is essential for reliable XCW results.
  • This work refines understanding and methodology in experimental charge density studies.