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

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.