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To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing...
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Updated: May 16, 2025

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Solid-state calculations for iterative refinement in quantum crystallography using the multipole model.

Michael Patzer1, Christian W Lehmann1

  • 1Chemische Kristallographie und Elektronenmikroskopie, Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr, 45470 North Rhine-Westphalia, Germany.

Iucrj
|April 4, 2025
PubMed
Summary
This summary is machine-generated.

A new quantum crystallographic method uses theoretical multipole parameters from solid-state calculations for accurate electron density refinement. This approach, implemented in ReCrystal, improves hydrogen atom positioning in molecular crystals.

Keywords:
CRYSTAL17ReCrystalcharge density analysismultipole modelquantum crystallographysolid-state calculationstransferable atom form factors

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Area of Science:

  • Quantum Crystallography
  • Solid-State Chemistry
  • Computational Materials Science

Background:

  • Accurate electron density description is crucial for understanding chemical bonding and intermolecular interactions.
  • Existing methods like Hirshfeld atom refinement (HAR) have limitations, particularly with gas-phase approximations.
  • Transferable form factor approaches offer potential but require careful implementation.

Purpose of the Study:

  • To develop and validate a novel quantum crystallographic refinement methodology.
  • To utilize theoretical multipole parameters directly from solid-state calculations.
  • To improve the accuracy of electron density refinement and hydrogen atom positioning in molecular crystals.

Main Methods:

  • Development of the Python3 code ReCrystal for iterative refinement.
  • Generation of theoretical multipole parameters using CRYSTAL17 and the XD program.
  • Application of the method to molecular crystals of D/L-serine and xylitol.

Main Results:

  • The ReCrystal method provides refinement comparable to existing transferable form factor approaches.
  • Accurate determination of hydrogen atom positions in xylitol, showing good agreement with neutron diffraction data.
  • Demonstrated the effectiveness of periodic boundary conditions in ReCrystal for molecular crystal refinement.

Conclusions:

  • The developed methodology offers a robust alternative for charge density studies, particularly focusing on weak interactions.
  • ReCrystal allows for multipole parameters derived from high-resolution calculated diffraction data without database dependency.
  • This approach effectively separates model and experimental errors, enhancing refinement reliability.