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Crystal Density01:19

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The crystal lattice structure of a material allows us to determine how many molecules exist in its unit cell. With this information, alongside the unit-cell parameters - three distance parameters (a, b, c) and three angular parameters (α, β, γ).Density (ρ) = (Z × M) / (a × b × c × NA)where:Z is the number of formula units per unit cellM is the molar mass of the substancea, b, and c are the edge lengths of the unit cellNA is Avogadro’s numberFor a simple cubic lattice, atoms are located only at...
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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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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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Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
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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...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Improving density functional theory for crystal polymorph energetics.

Christopher R Taylor1, Peter J Bygrave, Judy N Hart

  • 1Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, UK.

Physical Chemistry Chemical Physics : PCCP
|March 9, 2012
PubMed
Summary
This summary is machine-generated.

Density functional theory (DFT) predictions for crystalline para-diiodobenzene (PDIB) polymorph stability are significantly improved with a two-body correction. This enhanced DFT method accurately predicts the stable polymorph, aligning with experimental and benchmark quantum Monte Carlo results.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Solid-State Physics

Background:

  • Density Functional Theory (DFT) is widely used for predicting material properties.
  • Accurate prediction of crystalline polymorph relative stabilities is crucial in materials science.
  • Previous DFT studies showed significant variability in predicting para-diiodobenzene (PDIB) polymorph stability.

Purpose of the Study:

  • To improve the accuracy of DFT predictions for the relative stabilities of PDIB polymorphs.
  • To validate a simple two-body correction method using wavefunction-based electronic structure theory.
  • To compare computational results with experimental data and benchmark quantum Monte Carlo (QMC) calculations.

Main Methods:

  • Employed a two-body correction scheme incorporating Grimme's spin-scaled second-order Møller-Plesset perturbation theory (MP2).
  • Applied the corrected scheme in conjunction with various density functionals for DFT calculations.
  • Calculated the relative stabilities of the two known ambient polymorphs of para-diiodobenzene (PDIB).

Main Results:

  • The two-body corrected DFT scheme dramatically improved the prediction quality for PDIB polymorph stabilities.
  • The corrected method consistently predicted the alpha-polymorph as more stable, in agreement with experimental observations.
  • The calculated relative stability closely matched benchmark Quantum Monte Carlo (QMC) results within statistical uncertainty.

Conclusions:

  • A simple two-body correction significantly enhances DFT accuracy for crystalline polymorph relative stabilities.
  • The improved method provides reliable predictions for PDIB polymorph stability, consistent with experimental and high-level theoretical data.
  • This approach offers a more robust computational tool for predicting the behavior of crystalline materials.