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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

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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...
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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 the dxy,...
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Most elements exist in nature as a mixture of isotopes. The isotopes differ in weight due to their respective number of neutrons. The molecular weight of a molecule is different depending on the specific isotope of its elements involved. As a result, the mass spectrum of the molecule exhibits peaks from the same fragment at multiple positions. The positions of these mass signals depend on the difference between the molecular mass. Furthermore, the intensity of these signals is dependent on the...
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Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
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Trends in Lattice Energy: Ion Size and Charge02:54

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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Related Experiment Video

Updated: Sep 22, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Improved volume variable cluster model method for crystal-lattice optimization: effect on isotope fractionation

Yan-Fang Wang1, Xin-Yue Ji1, Le-Cai Xing1,2

  • 1School of Earth Science and Engineering, Hebei University of Engineering, Handan, 056038, China.

Geochemical Transactions
|May 22, 2022
PubMed
Summary
This summary is machine-generated.

The improved volume variable cluster model (VVCM) accurately optimizes molecular clusters for calculating isotope fractionation factors. This method enhances accuracy for bond lengths and thermodynamic parameters in various minerals and solutions.

Keywords:
Geometric optimizationIsotopic equilibrium fractionation factorMolecular clusterRelative volume changeVVCM

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Area of Science:

  • Geochemistry
  • Computational Chemistry
  • Mineral Physics

Background:

  • Accurate calculation of isotopic fractionation factors and element partition coefficients relies on precise geometric optimization of molecular clusters.
  • Geometric optimization influences critical parameters like average bond length, molecular volume, and vibrational frequencies, impacting thermodynamic calculations.

Purpose of the Study:

  • To evaluate and apply an improved volume variable cluster model (VVCM) for accurate geometric optimization of molecular clusters.
  • To calculate equilibrium isotope fractionation factors for silicon and oxygen in quartz, and for Cd and Zn in hydroxide and carbonate minerals.
  • To re-evaluate published theoretical results for cadmium-containing hydroxyapatite using the refined VVCM method.

Main Methods:

  • Utilized the improved volume variable cluster model (VVCM) for geometric optimization of molecular clusters, including quartz, Zn-Al layered double hydroxide, and cadmium-containing calcite.
  • Calculated average bond lengths, relative volume changes, and harmonic vibrational frequencies.
  • Determined equilibrium isotope fractionation factors at 298 K for specified mineral-solution systems and re-evaluated published data for cadmium-containing hydroxyapatite.

Main Results:

  • The improved VVCM method successfully optimized molecular clusters, yielding accurate average bond lengths (e.g., Si-O in quartz: 1.63 Å; Zn-O in Zn-Al LDH: 2.10 Å; Cd-O in calcite: 2.28 Å) and low relative volume changes.
  • Calculated equilibrium isotope fractionation factors for Si-O, Cd, and Zn were consistent with previous studies.
  • Relative volume changes obtained via VVCM were significantly lower than those from periodic boundary methods.

Conclusions:

  • The improved VVCM method demonstrates high reliability for geometric optimization of molecular clusters and accurate calculation of isotope fractionation factors.
  • The method provides a robust approach for studying isotopic behavior in various mineral systems under superficial conditions.
  • VVCM offers a valuable alternative to periodic boundary methods, particularly for calculating relative volume changes in molecular clusters.