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Crystal Field Theory - Tetrahedral and Square Planar Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...

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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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Related Experiment Video

Updated: Oct 7, 2025

Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source

Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source

Published on: April 23, 2021

A symmetry-orientated divide-and-conquer method for crystal structure prediction.

Xuecheng Shao¹, Jian Lv¹, Peng Liu¹

¹International Center of Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China.

The Journal of Chemical Physics

|January 9, 2022

Summary

This study introduces a novel symmetry-based method to simplify crystal structure prediction. The approach efficiently explores complex structures by focusing on high-symmetry subspaces, accelerating the discovery of new materials.

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Published on: July 21, 2017

Area of Science:

Materials Science
Computational Chemistry
Crystallography

Background:

Crystal structure prediction is crucial for materials discovery but computationally challenging due to high-dimensional potential energy surfaces.
Existing methods struggle with complex structures and preserving crystal symmetry during exploration.

Purpose of the Study:

To develop a novel, efficient, and symmetry-aware method for predicting complex crystal structures.
To simplify the global minimization problem in crystal structure prediction.

Main Methods:

A symmetry-orientated divide-and-conquer scheme to construct a symmetry tree graph.
Decomposition of the search space into symmetry-dependent subspaces.
An artificial intelligence-based symmetry selection strategy to explore low-lying, high-symmetry subspaces.

Main Results:

Successfully predicted candidate structures for binary Lennard-Jones mixtures.
Accurately predicted the high-pressure phase of ice with over 100 atoms.
Demonstrated simplification of crystal structure prediction by avoiding the complex P1 subspace.

Conclusions:

The proposed method effectively predicts complex crystal structures by leveraging symmetry.
This approach offers a significant advancement towards achieving reliable crystal structure prediction for complex systems.
Preserves crystal symmetry throughout the structure evolution process.