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Crystal Field Theory - Octahedral Complexes

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
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.
CFT focuses on...

Crystallographic Point Groups

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...

Determination of Crystal Structures

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
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...

X-ray Crystallography

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...

Molecular and Ionic Solids

Molecular and Ionic Solids

Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
Molecular Solids
Molecular crystalline solids, such as ice, sucrose (table sugar), and iodine, are solids that are composed of neutral molecules as their constituent units. These molecules are held together by weak intermolecular forces such as London dispersion forces, dipole-dipole interactions, or hydrogen bonds, which...

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Related Experiment Video

Updated: Apr 16, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Ab initio many-body quantum embedding and local correlation in crystalline materials using interpolative separable

Junjie Yang^1,2, Ning Zhang^1,3, Shunyue Yuan^2,4

¹Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

The Journal of Chemical Physics

|April 15, 2026

Summary

We developed an efficient quantum embedding method for periodic systems, reducing computational cost. This allows accurate calculation of correlated ground-state energies for solids, even in the thermodynamic limit.

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Last Updated: Apr 16, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

Computational Chemistry
Condensed Matter Physics
Quantum Mechanics

Background:

Accurate prediction of solid-state properties requires advanced quantum mechanical methods.
Infinite periodic systems pose significant computational challenges for traditional quantum chemistry approaches.

Purpose of the Study:

To present an efficient ab initio many-body quantum embedding method for periodic systems.
To reduce the computational scaling of these methods with respect to k-points.

Main Methods:

Translational symmetry adapted interpolative separable density fitting.
Density matrix embedding and local natural orbital correlation frameworks.
Coupled cluster calculations for weakly and strongly correlated solids.

Main Results:

Achieved linear scaling with the number of k-points for quantum embedding calculations.
Computed correlated ground-state coupled cluster energies for solids using up to 1000 k-points.
Extrapolated to obtain accurate ground-state energies in the thermodynamic limit.

Conclusions:

The developed method offers an efficient and accurate approach for studying electronic correlations in periodic materials.
Enables high-accuracy calculations of solid-state properties previously inaccessible due to computational cost.