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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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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Bewley Lattice Diagram01:12

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The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
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Crystal Field Theory
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CFT focuses on...
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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
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Correlation matrix renormalization theory in multi-band lattice systems.

Jun Liu1, Xin Zhao1, Yongxin Yao1

  • 1Ames Laboratory-U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|October 5, 2020
PubMed
Summary

A new computational method, correlation matrix renormalization (CMR), accurately describes electron correlation in materials. This efficient, parameter-free approach shows promise for predicting material properties across various electronic correlation strengths.

Keywords:
Gutzwiller approximationab initiocorrelation matrix renormalization theory (CMR)equilibrium lattice constant, cohesive energy, bulk modulusmultiband Gutzwiller trial wavefunction

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Area of Science:

  • Condensed Matter Physics
  • Computational Materials Science
  • Quantum Chemistry

Background:

  • Accurate treatment of electronic correlation is crucial for predicting material properties.
  • Existing methods like LDA+U and DFT+DMFT face challenges such as adjustable parameters and double-counting issues.
  • The correlation matrix renormalization (CMR) theory has shown promise in molecular systems.

Purpose of the Study:

  • To provide a detailed formulation and computational code implementation of CMR for multi-band periodic lattice systems.
  • To assess the efficiency and accuracy of the lattice CMR ab initio theory.
  • To compare CMR with other established methods for correlated-electron materials.

Main Methods:

  • Detailed theoretical formulation of CMR for periodic lattice systems.
  • Implementation of a computational code for lattice CMR calculations.
  • Benchmark studies on materials with s and p orbitals, varying electron correlation levels.

Main Results:

  • The lattice CMR ab initio theory is highly efficient and free of material-specific adjustable parameters.
  • CMR avoids the double-counting issues inherent in hybrid approaches like LDA+U and DFT+DMFT.
  • Benchmark studies demonstrate consistent performance of CMR for s and p orbital systems, from bonding to bond-breaking regions.

Conclusions:

  • The developed lattice CMR theory offers an efficient and accurate approach for studying correlated-electron materials.
  • CMR presents a viable alternative to existing methods, overcoming key limitations.
  • The implementation shows robust performance across a range of electron correlation scenarios.