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Updated: Jul 4, 2025

Measuring the Complete-arch Distortion of an Optical Dental Impression
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Van Vleck analysis of angularly distorted octahedra using VanVleckCalculator.

Liam A V Nagle-Cocco1, Siân E Dutton1

  • 1Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.

Journal of Applied Crystallography
|February 7, 2024
PubMed
Summary

This study introduces a new method for calculating Van Vleck modes in distorted octahedra, overcoming limitations of previous approaches. A Python package, VanVleckCalculator, is presented to analyze octahedral distortions, including shear and angular effects.

Keywords:
Jahn–Teller distortioncrystal structurecrystallographic softwareoctahedral distortionoctahedral tilting

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Area of Science:

  • Crystallography
  • Solid-state chemistry
  • Computational chemistry

Background:

  • Van Vleck modes analyze ligand displacements in octahedra, crucial for understanding Jahn-Teller distortions.
  • Current methods often neglect angular distortion, losing information on octahedral shear modes (Q4, Q5, Q6).

Purpose of the Study:

  • To discuss the validity of orthogonal bond length assumptions for Van Vleck mode calculation.
  • To present a novel method for calculating Van Vleck modes that incorporates angular distortion.
  • To introduce the VanVleckCalculator Python package for this purpose.

Main Methods:

  • Discussing the orthogonality assumption in bond length calculations.
  • Developing a new method to include angular distortion in Van Vleck mode analysis.
  • Implementing the method in the VanVleckCalculator Python package.

Main Results:

  • A method is presented to calculate Van Vleck modes without disregarding angular distortion.
  • The VanVleckCalculator package is introduced for analyzing octahedral distortions.
  • Octahedral shear and angular distortion are often correlated, predictable by the shear fraction parameter η.

Conclusions:

  • The new method provides a more complete analysis of octahedral distortions.
  • The VanVleckCalculator package facilitates accurate determination of Van Vleck modes.
  • The shear fraction parameter η aids in predicting correlations between shear and angular distortion under varying conditions.